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Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
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[1/1 Formula]
Work: Calculate the value of equation C(5,0)*2^0+C(5,1)*2^1+C(5,2)*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5 .
Question type: Mathematical calculation
Solution:
C(5,0)*2^0+C(5,1)*2^1+C(5,2)*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5
=1*2^0+C(5,1)*2^1+C(5,2)*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5
=1*2^0+5*2^1+C(5,2)*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5
=1*2^0+5*2^1+10*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5
=1*2^0+5*2^1+10*2^2+10*2^3+C(5,4)*2^4+C(5,5)*2^5
=1*2^0+5*2^1+10*2^2+10*2^3+5*2^4+C(5,5)*2^5
=1*2^0+5*2^1+10*2^2+10*2^3+5*2^4+1*2^5
=1*1+5*2^1+10*2^2+10*2^3+5*2^4+1*2^5
=1*1+5*2+10*2^2+10*2^3+5*2^4+1*2^5
=1*1+5*2+10*4+10*2^3+5*2^4+1*2^5
=1*1+5*2+10*4+10*8+5*2^4+1*2^5
=1*1+5*2+10*4+10*8+5*16+1*2^5
=1*1+5*2+10*4+10*8+5*16+1*32
=1+5*2+10*4+10*8+5*16+1*32
=1+10+10*4+10*8+5*16+1*32
=1+10+40+10*8+5*16+1*32
=1+10+40+80+5*16+1*32
=1+10+40+80+80+1*32
=1+10+40+80+80+32
=11+40+80+80+32
=51+80+80+32
=131+80+32
=211+32
=243
Answer:C(5,0)*2^0+C(5,1)*2^1+C(5,2)*2^2+C(5,3)*2^3+C(5,4)*2^4+C(5,5)*2^5=243