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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=3.448423*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+3.482907*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+3.517736*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+3.552913*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+3.588442*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+9.067814
=14.771773+8.062715+8.550509+9.067814
=22.834488+8.550509+9.067814
=31.384997+9.067814
=40.452811
Answer:3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19=40.452811
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19 .
Question type: Mathematical calculation
Solution:
3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*(1+1%)^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*(1+5%)^19
=3*1.01^14*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*1.05^15+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.01^15*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*1.05^16+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.01^16*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*1.05^17+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.01^17*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*1.05^18+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.01^18*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*1.05^19
=3*1.149474213237623*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=3.448423*2.078928179411369+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+3*1.160968955369999*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+3.482907*2.182874588381937+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+3*1.172578644923699*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+3.517736*2.292018317801034+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+3*1.184304431372936*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+3.552913*2.406619233691086+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+3*1.196147475686665*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+3.588442*2.52695019537564
=7.169024+7.602749+8.062715+8.550509+9.067814
=14.771773+8.062715+8.550509+9.067814
=22.834488+8.550509+9.067814
=31.384997+9.067814
=40.452811
Answer:3*(1+1%)^14*(1+5%)^15+3*(1+1%)^15*(1+5%)^16+3*(1+1%)^16*(1+5%)^17+3*(1+1%)^17*(1+5%)^18+3*(1+1%)^18*(1+5%)^19=40.452811