# I Find the formula to express the infinite series...

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1. Jun 27, 2016

### maxhersch

The problem is to find the general term $a_n$ (not the partial sum) of the infinite series with a starting point n=1

$$a_n = \frac {8} {1^2 + 1} + \frac {1} {2^2 + 1} + \frac {8} {3^2 + 1} + \frac {1} {4^2 + 1} + \text {...}$$

The denominator is easy, just $n^2 + 1$ but I can't think of any way to get the numerator to alternate between 8 and 1.

2. Jun 27, 2016

### micromass

Staff Emeritus
$4.5 + 3.5(-1)^{n+1}$

3. Jun 27, 2016

### maxhersch

Never mind I figured it out $$a_n = \frac {9 - 7 \{ -1 \} ^n} {2 \{ 1 + n^2 \}}$$