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The sum to infinity of the following series $\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\ldots \ldots \ldots .$. shall be
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$1$
Given series
$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\ldots=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\ldots$
Obviously the sum of series upto infinity is 1.
$\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\ldots=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\ldots$
Obviously the sum of series upto infinity is 1.
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