Question 1133988
<br>
The sum<br>
1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100)<br>
is equal to<br>
1/2+2/2+3/2+...+99/2<br>
This is an arithmetic series with 99 terms; the sum is 99 times the average of the first and last:<br>
{{{99((1/2+99/2)/2) = 99*25 = 2475}}}