infinite sequences and series?

Question

is the sum of all terms from 2 to infinity of 1/n(n-1) convergent or divergent? If it is convergent, what is its sum?

Answer 1

1/(n*(n-1)) , The sum from 2 to infinity is convergent.

You can write as follows :
1 /[n*(n-1)] = 1/n-1 - 1/n
so this sum is 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +1/4 -1/5 + .....

which becomes 1-1/n
if n approaches infinity 1/n approaches 0

so this sum approaches 1.