Re : Calculate the sum of this infinite series

$1=1$

$\frac{1}{2}+$ $\frac{1}{3}+$ $\frac{1}{4}=$ $\frac{1}{4}+$ $\frac{1}{4}+$ $\frac{1}{3}+$ $\frac{1}{4}>1$

$\frac{1}{5}+\frac{1}{6}+....+\frac{1}{25}=\frac{1}{25}+\frac{1}{25}+\frac{1}{25}+\frac{1}{25}+\frac{1}{25}+\frac{1}{6}+...+\frac{1}{25}>1$

So, $\frac{1}{n}$ $+\frac{1}{n+1}+...\frac{1}{n^2}>1$

So, $1+\frac{1}{2}+\frac{1}{3}+.....>1+1+1+1.....=\boxed{infinite}$

Let S = (1/2 + 1/3 + 1/4 + 1/5. + 1/6...)
S is greater than (1/2 + 1/4 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1//9......) , this inturn is greater than
( 1/2 + 1/4 + 1/4 + 1/8+1/8+1/8+1/8 + 1/9...) or (1/2 + 2/4 + 4/8 + 8/16.....) or N/2 when N tends to infinity, S > N/2
So the LHS S is greater than N/2 when N tends to infinity so the LHS also tends to infinity for large values of nor number of terms. This series is actually divergent and the sum is infinity