Question 1200316
<br>
The numerators are the triangular numbers:
1
1+2=3
1+2+3=6
1+2+3+4=10
...<br>
The denominators are consecutive integers.<br>
The terms of the sequence are then<br>
{{{1/2}}} , {{{3/3}}} , {{{6/4}}} , {{{10/5}}} , ...<br>
Those are equivalent to<br>
{{{1/2}}}, {{{2/2}}}, {{{3/2}}}, {{{4/2}}}, ..., {{{99/2}}}<br>
The sum of all the terms is then the sum from n = 1 to 99 of (n/2):<br>
{{{sum(n/2,1,99)=((1/2)((99*100)/2))=99*25=2475}}}<br>
ANSWER: 2475<br>