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

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

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

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply p-Series Test:

converges

= \frac{1}{5} converges

= converges

f (x) = \frac{x ^{2} + 3}{x ^{2}}

y = cos^{2} (3 x - 1)

x \to 0 - lim (\frac{8}{5 x ^{\frac{1}{2}}})

(5.4) (7.7)

\int \frac{x ^{2}}{( 15 + 6 x - 9 x ^{2} ) ^{\frac{3}{2}}} d x

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