Consider the sequence (1/n^2)+(2/n^2)+...+(n/n^2).
What is the limit of the sequence?
1/n2 ( 1+2+3+...+ n)
=1/n^2 (n)(n+1)/2=1/n^2(n^2+n)/2
= (1+1/n)/2
check it. Let n=5
sum= 1/25 * (1+2+3+4+5)=15/25=3/5
by the formula, sum= 1/2 (1+1/5)=3/5
What is the limit of the sequence?
=1/n^2 (n)(n+1)/2=1/n^2(n^2+n)/2
= (1+1/n)/2
check it. Let n=5
sum= 1/25 * (1+2+3+4+5)=15/25=3/5
by the formula, sum= 1/2 (1+1/5)=3/5