What is the sum from n=0 to infinity of An*(-1)^n ?

The sum from n=0 to infinity of An*(-1)^n is diverges

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sum from n=0 to infinity of An*(-1)^n

n = 0 \sum \infty A n \cdot (- 1)^{n}

diverges

Solution steps

n = 0 \sum \infty A n (- 1)^{n}

Apply the constant multiplication rule:

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

= A \cdot n = 0 \sum \infty n (- 1)^{n}

Apply Series Divergence Test:

diverges

= A diverges

= diverges

k = 0 \sum \infty \frac{1}{k ^{2} + 4}

n = 3 \sum \infty \frac{1}{( n + 1 ) ^{2}}

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

n = 0 \sum \infty \frac{n}{9 ^{n}}

n = 0 \sum \infty \frac{2 n}{5 n - 3}

What is the sum from n=0 to infinity of An*(-1)^n ?
The sum from n=0 to infinity of An*(-1)^n is diverges