What is the sum from n=0 to infinity of 5/(1+2n^4) ?

The sum from n=0 to infinity of 5/(1+2n^4) is converges

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sum from n=0 to infinity of 5/(1+2n^4)

n = 0 \sum \infty \frac{5}{1 + 2 n ^{4}}

converges

Solution steps

n = 0 \sum \infty \frac{5}{1 + 2 n ^{4}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

= 5 \cdot n = 0 \sum \infty \frac{1}{1 + 2 n ^{4}}

Apply Series Comparison Test:

converges

= 5 converges

= converges

n = 2 \sum \infty (- 0.05)^{n}

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

n = 1 \sum \infty n! e^{- 3 n}

n = 0 \sum \infty cos (3 n)

n = 1 \sum \infty 2 n + i

What is the sum from n=0 to infinity of 5/(1+2n^4) ?
The sum from n=0 to infinity of 5/(1+2n^4) is converges