What is the sum from n=1 to infinity of 5*3^n ?

The sum from n=1 to infinity of 5*3^n is diverges

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sum from n=1 to infinity of 5*3^n

n = 1 \sum \infty 5 \cdot 3^{n}

diverges

Solution steps

n = 1 \sum \infty 5 \cdot 3^{n}

Apply the constant multiplication rule:

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

= 5 \cdot n = 1 \sum \infty 3^{n}

n = k \sum \infty (a_{n}) = n = 0 \sum \infty (a_{n}) - a_{0} - a_{1} - \dots a_{k - 1}

= 5 (n = 0 \sum \infty 3^{n} - 3^{0})

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

diverges

If part of the expression diverges, then entire expression diverges

= diverges

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What is the sum from n=1 to infinity of 5*3^n ?
The sum from n=1 to infinity of 5*3^n is diverges