JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q27

MathematicsInteger+4 / -1Question 27 of 90

Let $f(x)=2x^2-x-1$ and $S=\{n\in\mathbf Z:|f(n)|\le800\}$ . Then, the value of $\displaystyle\sum_{n\in S}f(n)$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 10620

Range. $2n^2-n-1\le800$ for $-19\le n\le20$ , and $f\ge-800$ always.

Sum. $\sum n^2=2\cdot2470+400=5340$ , $\sum n=20$ , 40 terms: $10680-20-40=10620$ .

Answer: 10620

JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 27