一道数列问题a(n)=(1/2)的n次方c(n)=1/(a(n)+1)-1/(a(n+1)-1)数列cn的前N项和味TN求证T(n)>2n-1/2不需要太太详细但能让我看懂

Question

一道数列问题
a(n)=(1/2)的n次方
c(n)=1/(a(n)+1)-1/(a(n+1)-1)
数列cn的前N项和味TN 求证T(n)>2n-1/2
不需要太太详细但能让我看懂

Answer 1

Cn=1/(1/2^n+1)-1/(1/2^(n+1)-1)彻底化简得(2^(2n+2)+2^n)/(2^(2n+1)+2^n-1)>(2^(2n+2)+2^n)/(2^(2n+1)+2^n)=(2^(n+2)+1)/(2^(n+1)+1)=2-1/(2^(n+1)-1)>2-1/2^(n+1)则∑Cn>∑(2-1/2^(n+1))=2n-1/2+1/2^(2n+1)>2n-1/2...