What is the sum from n=0 to infinity of 2(3/4)^n ?

The sum from n=0 to infinity of 2(3/4)^n is 8

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sum from n=0 to infinity of 2(3/4)^n

n = 0 \sum \infty 2 (\frac{3}{4})^{n}

8

Solution steps

n = 0 \sum \infty 2 (\frac{3}{4})^{n}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty (\frac{3}{4})^{n}

Apply Series Geometric Test:

4

= 2 \cdot 4

Simplify

= 8

n = 1 \sum \infty n e^{- 7 n^{2}}

k = 0 \sum \infty (0.6)^{k}

n = 1 \sum \infty \frac{n ^{2}}{7 ^{n}}

n = 0 \sum \infty \frac{4}{2 n + 3}

n = 0 \sum \infty 9^{- n}

What is the sum from n=0 to infinity of 2(3/4)^n ?
The sum from n=0 to infinity of 2(3/4)^n is 8