What is the sum from i=1 to infinity of 5*i ?

The sum from i=1 to infinity of 5*i is diverges

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sum from i=1 to infinity of 5*i

i = 1 \sum \infty 5 \cdot i

diverges

Solution steps

i = 1 \sum \infty 5 i

Apply the constant multiplication rule:

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

= 5 \cdot i = 1 \sum \infty i

Apply Series Divergence Test:

diverges

= 5 diverges

= diverges

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

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

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

n = 0 \sum \infty e^{- 21 n}

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

What is the sum from i=1 to infinity of 5*i ?
The sum from i=1 to infinity of 5*i is diverges