What is the sum from n=0 to infinity of n*2 ?

The sum from n=0 to infinity of n*2 is diverges

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sum from n=0 to infinity of n*2

n = 0 \sum \infty n \cdot 2

diverges

Solution steps

n = 0 \sum \infty n \cdot 2

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty n

Apply Series Divergence Test:

diverges

= 2 diverges

= diverges

n = 1 \sum \infty \frac{1}{3 n ^{5} + 7}

n = 1 \sum \infty \frac{3 n ^{2}}{2 i}

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

n = 0 \sum \infty (\frac{2 - 1}{2})^{n}

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

What is the sum from n=0 to infinity of n*2 ?
The sum from n=0 to infinity of n*2 is diverges