If the sum of the first 10 terms of the series

\(
\frac{1}{1+1^4 \times 4}+\frac{2}{1+2^4 \times 4}+\frac{3}{1+3^4 \times 4}+\frac{4}{1+4^4 \times 4}+\ldots \ldots
\)

is \(\frac{m}{n}, \operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to:

[JEE Main 2026, 5 Apr (Shift 2)]

Question

If the sum of the first 10 terms of the series

\(
\frac{1}{1+1^4 \times 4}+\frac{2}{1+2^4 \times 4}+\frac{3}{1+3^4 \times 4}+\frac{4}{1+4^4 \times 4}+\ldots \ldots
\)

is \(\frac{m}{n}, \operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to:

[JEE Main 2026, 5 Apr (Shift 2)]

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If the sum of the first 10 terms of the series \( \frac{1}{1+1^4 \times 4}+\frac{2}{1+2^4 \times 4}+\frac{3}{1+3^4 \time…