I need to find the result of the following series sum:
$\sum_{n=1}^{\infty} \dfrac{2}{4n^2+8n+3}$
Can someone help me?
2026-04-09 05:47:23.1775713643
Value of series sum question
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Hint:
The decomposition into partial fractions: $$\dfrac{2}{4n^2+8n+3}=\frac2{(2n+1)(2n+3)}=\frac A{2n+1}+\frac B{2n+3}$$ yields a telescoping series.