What is the sum from n=0 to infinity of (10^n)/(9^n) ?

The sum from n=0 to infinity of (10^n)/(9^n) is diverges

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sum from n=0 to infinity of (10^n)/(9^n)

n = 0 \sum \infty \frac{1 0 ^{n}}{9 ^{n}}

diverges

Solution steps

n = 0 \sum \infty \frac{1 0 ^{n}}{9 ^{n}}

n \to \infty lim (n (\frac{\frac{1 0 ^{n}}{9 ^{n}}}{\frac{1 0 ^{n + 1}}{9 ^{n + 1}}} - 1)) = - \infty

L < 1,

by the Raabe's test

= diverges

x^{3} + 3 y - x \frac{d y}{d x} = 0

y^{^{''}} + 36 y = 2 tan (6 x)

\frac{d}{d x} (e^{a r c t a n (x)})

\frac{\partial}{\partial x} (4 x^{3} - 3 x^{2} y + 5 x)

x - 1

What is the sum from n=0 to infinity of (10^n)/(9^n) ?
The sum from n=0 to infinity of (10^n)/(9^n) is diverges