What is the sum from n=0 to infinity of 7+5/(n^5) ?

The sum from n=0 to infinity of 7+5/(n^5) is diverges

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sum from n=0 to infinity of 7+5/(n^5)

n = 0 \sum \infty 7 + \frac{5}{n ^{5}}

diverges

Solution steps

n = 1 \sum \infty 7 + \frac{5}{n ^{5}}

Simplify

7 + \frac{5}{n ^{5}} : \frac{7 n ^{5} + 5}{n ^{5}}

= n = 1 \sum \infty \frac{7 n ^{5} + 5}{n ^{5}}

Apply Series Divergence Test:

diverges

= diverges

n = 1 \sum \infty (1.05)^{n}

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

k = 2 \sum \infty (\frac{3}{5})^{2 k}

m = 2 \sum \infty \frac{4}{3 ^{m}}

n = 1 \sum \infty n e^{(- n^{2})}

What is the sum from n=0 to infinity of 7+5/(n^5) ?
The sum from n=0 to infinity of 7+5/(n^5) is diverges