What is the sum from i=1 to infinity of 5*0.2^{i-1} ?

The sum from i=1 to infinity of 5*0.2^{i-1} is converges

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sum from i=1 to infinity of 5*0.2^{i-1}

i = 1 \sum \infty 5 \cdot 0. 2^{i - 1}

converges

Solution steps

i = 1 \sum \infty 5 \cdot 0. 2^{i - 1}

Apply the constant multiplication rule:

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

= 5 \cdot i = 1 \sum \infty 0. 2^{i - 1}

Apply Series Ratio Test:

converges

= 5 converges

= converges

n = 1 \sum \infty \frac{3}{5 ^{n + 2}}

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

n = 0 \sum \infty 5^{- 2 n + 1} 3^{n}

n = 1 \sum \infty n ln (1 + \frac{1}{n})

n = 1 \sum \infty 4^{3 - 3 n}

What is the sum from i=1 to infinity of 5*0.2^{i-1} ?
The sum from i=1 to infinity of 5*0.2^{i-1} is converges