The sum of the series $1/(1 + {1^2} + {1^4}) + 1/(1 + {2^2} + {2^4}) + 1/(1 + {3^2} + {3^4}) + ...$ to $n$ terms is

$\frac{{n\left( {{n^2} + 1} \right)}}{{{n^2} + n + 1}}$

$\frac{{n\left( {{n^2} - 1} \right)}}{{2({n^2} + n + 1)}}$

JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Easy

1 of 1

Analyzing +4 | -1

The sum of the series

1/(1 + {1^2} + {1^4}) + 1/(1 + {2^2} + {2^4}) + 1/(1 + {3^2} + {3^4}) + ...

n

terms is

View answer and explanation

Correct option: B

\frac{{n\left( {n + 1} \right)}}{{2({n^2} + n + 1)}}

Option B (

\frac{{n\left( {n + 1} \right)}}{{2({n^2} + n + 1)}}

) is correct because the series can be expressed as a telescoping series, allowing for simplification and calculation of the sum.

Practice All Chapter MCQs →

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\frac{3}{4}