Question

1/2+1/2的平方+1/2的立方+1/2的4次方+…+1/2的n次方=?

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Answer 1

1/2+1/4+1/8+1/16...+1/2^n
=2/4+1/4+1/8+1/16...+1/2^n
=3/4+1/8+1/16...+1/2^n
=6/8+1/8+1/16...+1/2^n
=7/8+1/16...+1/2^n
=(2^n-1)/2^n
=1 - 1/2^n

Answer 2

令S=1/2+(1/2)^2+1/3)^3+……+（1/2）^(n-1)+(1/2)^n
2S=1+1/2+(1/2)^2+……+（1/2）^(n-1)
S=2S-S=1-(1/2)^n

Answer 3

等比数列，公比q为二分之一，1减0.5分之0.5乘以括号1减0.5的n次方括号。