What is the sum from k=n to infinity of (3/4)^k(1/4) ?

The sum from k=n to infinity of (3/4)^k(1/4) is converges

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sum from k=n to infinity of (3/4)^k(1/4)

k = n \sum \infty (\frac{3}{4})^{k} (\frac{1}{4})

converges

Solution steps

k = n \sum \infty (\frac{3}{4})^{k} \frac{1}{4}

Apply the constant multiplication rule:

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

= \frac{1}{4} \cdot k = n \sum \infty (\frac{3}{4})^{k}

Apply Series Ratio Test:

converges

= \frac{1}{4} converges

= converges

What is the sum from k=n to infinity of (3/4)^k(1/4) ?
The sum from k=n to infinity of (3/4)^k(1/4) is converges