# Find a formula for the general term anan (not the partial sum) of the infinite series. Assume the infinite series begins at n=1. frac{2}{1^2+1}+frac{1}{2^2+1}+frac{2}{3^2+1}+frac{1}{4^2+1}+...

Find a formula for the general term anan (not the partial sum) of the infinite series. Assume the infinite series begins at n=1.
$\frac{2}{{1}^{2}+1}+\frac{1}{{2}^{2}+1}+\frac{2}{{3}^{2}+1}+\frac{1}{{4}^{2}+1}+...$
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Arnold Odonnell
In the given infinite series, find the term of the series
The terms of the series is given as:
${a}_{1}=\frac{2}{{1}^{2}+1}$
${a}_{2}=\frac{1}{{2}^{2}+1}$
${a}_{3}=\frac{2}{{3}^{2}+1}$
Here we can see that denominator of each term of the series is represented as $\left({n}^{2}+1\right)$:
The numerator of the series is the repetition of 2,1,2,1…
Let the terms of the series is calculated as:
when n is odd then k=2
when n is even then k=1
Jeffrey Jordon