设x1=1x2=-1.,xn=∑k=31/k(k+1),n=3,4.求极限

Question

设x1=1 x2=-1 .,xn=∑k=3 1/k(k+1) ,n=3,4 .
求极限

Answer 1

lim(n->∞) xn=lim(n->∞) [1/3*4+1/4*5+...+1/n(n+1)]
=lim(n->∞) [1/3-1/4+1/4-1/5+...+1/n-1/(n+1)]
=lim(n->∞) [1/3-1/(n+1)]
=1/3