lim(n趋于无穷)(1/3+1/15+...+1/4n2-1)=多少

Question

lim(n趋于无穷)(1/3+1/15+...+1/4n2-1)=多少

Answer 1

4n^2-1=0.5*[1/(2n-1)-1/(2n+1)]
lim(1/3+1/5+...+1/4n^2-1)=lim0.5[(1-1/3)+(1/3-1/5)+.+(1/2n-1+1/2n+1)]
0.5lim[1-1/2n+1]=0.5