What is the sum from n=0 to infinity of 1/(1+3n^4) ?

The sum from n=0 to infinity of 1/(1+3n^4) is converges

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sum from n=0 to infinity of 1/(1+3n^4)

n = 0 \sum \infty \frac{1}{1 + 3 n ^{4}}

converges

Solution steps

n = 0 \sum \infty \frac{1}{1 + 3 n ^{4}}

Apply Series Comparison Test:

converges

= converges

n = 1 \sum \infty (\frac{1}{1 + n})^{n}

n = 0 \sum \infty 2 \cdot 2^{n}

n = 0 \sum \infty 2 + \frac{( - 1 ) ^{n}}{n}

n = 0 \sum \infty \frac{11}{2 n - 1}

n = 1 \sum \infty (\frac{n}{10})^{n}

What is the sum from n=0 to infinity of 1/(1+3n^4) ?
The sum from n=0 to infinity of 1/(1+3n^4) is converges