1+1/4+1/12+…+1/(2n^2-2n),等于多少?

Question

1+1/4+1/12+…+1/(2n^2-2n),等于多少?

Answer 1

1/(2n^2-2n)=(1/2)/(n(n-1))=(1/2)[1/(n-1) - 1/n]
则和式=(1/2)[(1/1 - 1/2)+(1/2 - 1/3)+...+1/(n-1) - 1/n]
=(1/2)(1 - 1/n)