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Q.
$\sqrt{1+2(0.4)+3(0.4)^2+4(0.4)^3+\ldots \ldots \infty}$ has the value equal to
Sequences and Series
Solution:
$ 1+2 x +3 x ^2+4 x ^3+\ldots \ldots \infty=\frac{1}{(1- x )^2}$
$\therefore \text { square root is } \frac{1}{1- x }=\frac{1}{1-0.4}=\frac{1}{0.6}=\frac{5}{3}$