# Find the values of x for which the series 1/x + 1/x^2 + 1/x^3+… converges and express the sum as a function of x | infinite series problems and solutions

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# Find the values of x for which the series 1/x + 1/x^2  + 1/x^3+…  converges and express the sum as a function of x

\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}+...

Related  Discuss the nature of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 … Or Discuss the Convergency of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 … Or test the Convergence of the series 1/1.2 +1/2.3 + 1/3.4 + 1/4.5 …

## The geometric sum formula for infinite terms is given as:

If  common ration |r| < 1, S_\infty=\frac{a}{1-r}

Where

## This is a geometric series with ratio 1/x. It converges for |1/x|<1  that is , for |x|>1 The sum is

\frac{\frac{1}{x}}{1-\frac{1}{x}}=\frac{1}{x-1}

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