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

The sum from n=0 to infinity of (A/(A+1))^n is converges

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sum from n=0 to infinity of (A/(A+1))^n

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

converges

Solution steps

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

n \to \infty lim (n (\frac{( \frac{A}{A + 1} ) ^{n}}{( \frac{A}{A + 1} ) ^{n + 1}} - 1)) = \infty

L > 1,

by the Raabe's test

= converges

f (x) = e^{9 x}

f (x) = 3 x^{2} + 4 x, at x = - 2

x \to 0 lim (cos (\frac{7}{x}))

x \to 9 lim (81 - x^{2})

What is the sum from n=0 to infinity of (A/(A+1))^n ?
The sum from n=0 to infinity of (A/(A+1))^n is converges