What is the sum from n=1 to infinity of (100)(1/2)^n ?

The sum from n=1 to infinity of (100)(1/2)^n is 100

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sum from n=1 to infinity of (100)(1/2)^n

n = 1 \sum \infty (100) (\frac{1}{2})^{n}

100

Solution steps

n = 1 \sum \infty 100 (\frac{1}{2})^{n}

Apply the constant multiplication rule:

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

= 100 \cdot n = 1 \sum \infty (\frac{1}{2})^{n}

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

= 100 (n = 0 \sum \infty (\frac{1}{2})^{n} - (\frac{1}{2})^{0})

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

= 100 (2 - (\frac{1}{2})^{0})

Simplify

= 100

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What is the sum from n=1 to infinity of (100)(1/2)^n ?
The sum from n=1 to infinity of (100)(1/2)^n is 100