Find the sum of the series - 132-1-142-2-152-3-162-4-

∑_n=2^∞1n^2+3n Neglecting Higher values 110+118+128+140+154+170+188+1108+1130=0.2758 ...

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Summation by Sigma Method

Find the sum ...

Question

Find the sum of the series : $\frac{1}{3^{2} + 1} + \frac{1}{4^{2} + 2} + \frac{1}{5^{2} + 3} + \frac{1}{6^{2} + 4} + . . . \infty$

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\frac{1}{3^{2} + 1} + \frac{1}{4^{2} + 2} + \frac{1}{5^{2} + 3} + \frac{1}{6^{2} + 4} + . . . . . \infty

\frac{1}{3^{2} + 1} + \frac{1}{4^{2} + 2} + \frac{1}{5^{2} + 3} + \frac{1}{6^{2} + 4}

\infty

1 + 2 x + \frac{2^{2} - 1}{⌊ 2} \cdot \frac{x^{2}}{1} + \frac{3^{2} - 1}{⌊ 3} \cdot \frac{x^{3}}{2} + \frac{4^{2} - 1}{⌊ 4} \cdot \frac{x^{4}}{3} + . . . . .

1 \cdot 2^{2} + 2 \cdot 3^{2} + 3 \cdot 4^{2} + 4 \cdot 5^{2} + \dots

n

1^{2} - 2^{2} + 3^{2} - 4^{2} + 5^{2} - 6^{2} + \dots

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