What is the sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3)) ?

The sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3)) is converges

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sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3))

n = 1 \sum \infty \frac{( ( - 1 ) ^{(n - 1)} )}{( n ^{3} )}

converges

Solution steps

n = 1 \sum \infty \frac{( - 1 ) ^{n - 1}}{n ^{3}}

Simplify

(- 1)^{n - 1} : (- 1)^{n} (- 1)^{- 1}

= n = 1 \sum \infty \frac{( - 1 ) ^{n} ( - 1 ) ^{- 1}}{n ^{3}}

Apply the constant multiplication rule:

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

= (- 1)^{- 1} \cdot n = 1 \sum \infty \frac{( - 1 ) ^{n}}{n ^{3}}

(- 1)^{- 1} = - 1

= (- 1) \cdot n = 1 \sum \infty \frac{( - 1 ) ^{n}}{n ^{3}}

Apply Alternating Series Test:

converges

= (- 1) converges

= converges

y^{^{'}} + 2 y = 3

x \to 2 - lim (2 - x)

x \to 2 - lim (\frac{1}{x - 2})

f (x) = 2 x, at x = 1

(ln (x))^{6}

What is the sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3)) ?
The sum from n=1 to infinity}(((-1)^{(n-1) of))/((n^3)) is converges