What is the sum from n=1 to infinity of 7(-4)^{n-1} ?

The sum from n=1 to infinity of 7(-4)^{n-1} is diverges

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sum from n=1 to infinity of 7(-4)^{n-1}

n = 1 \sum \infty 7 (- 4)^{n - 1}

diverges

Solution steps

n = 1 \sum \infty 7 (- 4)^{n - 1}

Apply the constant multiplication rule:

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

= 7 \cdot n = 1 \sum \infty (- 4)^{n - 1}

Apply Series Ratio Test:

diverges

= 7 diverges

= diverges

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What is the sum from n=1 to infinity of 7(-4)^{n-1} ?
The sum from n=1 to infinity of 7(-4)^{n-1} is diverges