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

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

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sum from n=0 to infinity of 2/(n^2)

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

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply p-Series Test:

converges

= 2 converges

= converges

\int_{- 4}^{2} (x + 4) d x

y^{2} = 4 x, y = x^{2}

8 x^{2} - 2, at x = - 4

x^{4} + 2 x^{2} + 3, at x = - 2

f (x) = 4 e^{2 x^{3}}

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