What is the sum from n=0 to infinity of (-3/2)^n ?

The sum from n=0 to infinity of (-3/2)^n is diverges

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sum from n=0 to infinity of (-3/2)^n

n = 0 \sum \infty (- \frac{3}{2})^{n}

diverges

Solution steps

n = 0 \sum \infty (- \frac{3}{2})^{n}

(- \frac{3}{2})^{n} = 1. 5^{n} (- 1)^{n}

= n = 0 \sum \infty 1. 5^{n} (- 1)^{n}

Apply Series Ratio Test:

diverges

= diverges

y = 5 x - x^{2}, y = x

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

\frac{d}{d x} (x x^{2} + y^{2} + z^{2})

\frac{d}{d x} (4 x sin (π x))

What is the sum from n=0 to infinity of (-3/2)^n ?
The sum from n=0 to infinity of (-3/2)^n is diverges