JEE Mains · Maths · STD 11 - 8. sequence and series
If \(\sum_{k=1}^{10} \frac{k}{k^{4}+k^{2}+1}=\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m+n\) is equal to.
- A \(166\)
- B \(165\)
- C \(166\)
- D \(167\)
Answer & Solution
Correct Answer
(A) \(166\)
Step-by-step Solution
Detailed explanation
\(\sum_{ k =1}^{10} \frac{ k }{ k ^{4}+ k ^{2}+1}=\frac{ m }{ n }\) \(\Rightarrow \frac{1}{2} \sum_{ k =1}^{10} \frac{\left( k ^{2}+ k +1\right)-\left( k ^{2}- k +1\right)}{\left( k ^{2}+ k +1\right)\left( k ^{2}- k +1\right)}\)…
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