JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

If $\displaystyle\sum_{k=1}^{10}\frac{k}{k^4+k^2+1}=\frac mn$ , where $m$ and $n$ are co-prime, then $m+n$ is equal to ______

Your answer

Answer and worked solution

Official answer: 166

Split. $\frac k{k^4+k^2+1}=\frac12\left[\frac1{k^2-k+1}-\frac1{k^2+k+1}\right]$ , and $k^2+k+1$ is the next term's $k^2-k+1$ .

Telescope. $\frac12\left(1-\frac1{111}\right)=\frac{55}{111}$ , so $m+n=166$ .

Answer: 166

JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 24