What is the sum from n=1 to infinity of 5/(n^e) ?

The sum from n=1 to infinity of 5/(n^e) is converges

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sum from n=1 to infinity of 5/(n^e)

n = 1 \sum \infty \frac{5}{n ^{e}}

converges

Solution steps

n = 1 \sum \infty \frac{5}{n ^{e}}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty \frac{1}{n ^{e}}

Apply p-Series Test:

converges

= 5 converges

= converges

n = 1 \sum \infty \frac{0 ^{n}}{n !}

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

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

x = 0 \sum \infty x

n = 0 \sum \infty 3 n - 3

What is the sum from n=1 to infinity of 5/(n^e) ?
The sum from n=1 to infinity of 5/(n^e) is converges