Question

求和:3/2+13/4+41/8+.+[(2n-1)+1/2n]

Answer 1

对[(2n-1)+1/2^n] 各项分别求和即可

(2n-1)是奇数的和,=n^2

1/2^n是首项为1/2,公式为1/2的等比数列,其和是 1/2*(1-(1/2)^n)/(1-1/2)=1-1/2^n

所以原式=n^2+1-1/2^n