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It supports mathematical functions (including trigonometric functions).
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 C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6 .
Question type: Mathematical calculation
Solution:
C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*32+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*32+1*64
=1+6*2+15*4+20*8+15*16+6*32+1*64
=1+12+15*4+20*8+15*16+6*32+1*64
=1+12+60+20*8+15*16+6*32+1*64
=1+12+60+160+15*16+6*32+1*64
=1+12+60+160+240+6*32+1*64
=1+12+60+160+240+192+1*64
=1+12+60+160+240+192+64
=13+60+160+240+192+64
=73+160+240+192+64
=233+240+192+64
=473+192+64
=665+64
=729
Answer:C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6=729
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6 .
Question type: Mathematical calculation
Solution:
C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+C(6,5)*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+C(6,6)*2^6
=1*2^0+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2^1+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*2^2+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*2^3+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*2^4+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*2^5+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*32+1*2^6
=1*1+6*2+15*4+20*8+15*16+6*32+1*64
=1+6*2+15*4+20*8+15*16+6*32+1*64
=1+12+15*4+20*8+15*16+6*32+1*64
=1+12+60+20*8+15*16+6*32+1*64
=1+12+60+160+15*16+6*32+1*64
=1+12+60+160+240+6*32+1*64
=1+12+60+160+240+192+1*64
=1+12+60+160+240+192+64
=13+60+160+240+192+64
=73+160+240+192+64
=233+240+192+64
=473+192+64
=665+64
=729
Answer:C(6,0)*2^0+C(6,1)*2^1+C(6,2)*2^2+C(6,3)*2^3+C(6,4)*2^4+C(6,5)*2^5+C(6,6)*2^6=729