Question

数列1/(2^n-1)求和,或证明其和小于5/3.

Answer 1

n=1,2时,结论显然成立,

n≥3时,

2^n-1

＞2^n-2^(n-2)

＞3·2^(n-2)

Sn＜1+1/3+1/3·[1/2+1/4+1/8+……+1/2^(-2)]

=5/3-1/[3·2^(n-2)]

＜5/3