Question

数列bn=1/(n(n+1)) 求bn的前N项的和,要有证明过程 Tn=n/(n+1)

Answer 1

n=1/(n(n+1))=(1/n)-(1/(n+1))

Tn=(1/1)-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/n)-(1/(n+1))

=1-(1/(n+1))

=n/(n+1)