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Popular >

sum from k=1 to infinity of 0.5^k

Solution

k = 1 \sum \infty 0. 5^{k}

Solution

1

Solution steps

k = 1 \sum \infty 0. 5^{k}

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

= k = 0 \sum \infty 0. 5^{k} - 0. 5^{0}

k = 0 \sum \infty 0. 5^{k} = 2

= 2 - 0. 5^{0}

Simplify

= 1

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Frequently Asked Questions (FAQ)

What is the sum from k=1 to infinity of 0.5^k ?
The sum from k=1 to infinity of 0.5^k is 1