Sequence

[narik11]

For every positive integer n, if the nth term of the sequence is Xn=1/(n+1)(n+2)
then X1+X2+...X5=?

[Rahul@gurome]

Xn = 1/(n+1)(n+2) = 1/(n+1) - 1/(n+2).
So x1 = ½ - 1/3.
X2 = 1/3 - ¼.
X3 = ¼ - 1/5.
X4 = 1/5 - 1/6
X5 = 1/6 - 1/7.

Or x1+x2+x3+x4+x5 = ½ - 1/7 = 5/14.