JEE Mains · Maths · STD 11 - 8. sequence and series
The sum to \(10\) terms of the series \(\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\ldots\). is:-
- A \(\frac{59}{111}\)
- B \(\frac{55}{111}\)
- C \(\frac{56}{111}\)
- D \(\frac{58}{111}\)
Answer & Solution
Correct Answer
(B) \(\frac{55}{111}\)
Step-by-step Solution
Detailed explanation
\(T_r= \frac{\left( r ^2+ r +1\right)-\left( r ^2- r +1\right)}{2\left( r ^4+ r ^2+1\right)}\) \(\Rightarrow T _r=\frac{1}{2}\left[\frac{1}{ r ^2- r +1}-\frac{1}{ r ^2+ r +1}\right]\) \(T_1=\frac{1}{2}\left[\frac{1}{1}-\frac{1}{3}\right]\)…
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