JEE Mains · Maths · STD 11 - 8. sequence and series
If \(\sum_{r=1}^{25}\left(\frac{r}{r^{4}+r^{2}+1}\right)=\frac{p}{q}\) where p and q are positive integers such that gcd(p,q)=1, then \(p+q\) is equal to ____.
- A 976
- B 975
- C 977
- D 974
Answer & Solution
Correct Answer
(A) 976
Step-by-step Solution
Detailed explanation
\(S=\sum \frac{r}{\left(r^2+r+1\right)\left(r^2-r+1\right)}\) \(=\frac{1}{2} \sum_{ r =1}^{25}\left(\frac{1}{ r ^2- r +1}-\frac{1}{ r ^2+ r +1}\right)\)…
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