What is the sum from n=0 to infinity of 3/(n^4) ?

The sum from n=0 to infinity of 3/(n^4) is converges

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sum from n=0 to infinity of 3/(n^4)

n = 0 \sum \infty \frac{3}{n ^{4}}

converges

Solution steps

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

Apply the constant multiplication rule:

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

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

Apply p-Series Test:

converges

= 3 converges

= converges

\frac{d}{d x} (x cos (x) - sin (x))

\int sin (t) cos (n t) d t

y^{^{''}} - 3 y^{^{'}} = e^{3 t}

k = 1 \sum \infty \frac{5 + ( - 2 ) ^{k}}{4 ^{k + 1}}

\int \frac{sin ^{7} ( 12 x )}{cos ^{4} ( 12 x )} d x

What is the sum from n=0 to infinity of 3/(n^4) ?
The sum from n=0 to infinity of 3/(n^4) is converges