What is the sum from n=0 to infinity of ((2-1)/2)^n ?

The sum from n=0 to infinity of ((2-1)/2)^n is 2

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sum from n=0 to infinity of ((2-1)/2)^n

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

2

Solution steps

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

Simplify

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

Apply Series Geometric Test:

2

= 2

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

n = 4 \sum \infty \frac{4}{( n ^{2} - 1 )}

n = 1 \sum \infty \frac{n + 8}{n ^{2}}

n = 0 \sum \infty \frac{i ^{2 n}}{4 n}

n = 1 \sum \infty n (\frac{1}{7})^{n}

What is the sum from n=0 to infinity of ((2-1)/2)^n ?
The sum from n=0 to infinity of ((2-1)/2)^n is 2