Browse Questions

# Sum of n terms of the series $\large\frac{1}{4}+\large\frac{7}{16}+\large\frac{37}{64}+\large\frac{175}{256}$+... is

$(a)\;n-3^{-n}+1\qquad(b)\;n-4^{-n}+3^{-n}\qquad(c)\;n-3(1-(\large\frac{3}{4})^n)\qquad(d)\;n-((\large\frac{4}{3})^n-1)$

Answer : (c) $\;n-3(1-(\large\frac{3}{4})^n)$
Explanation : $\;r^{th}\;term\;of\;series$
$a_{r}=1-(\large\frac{3}{4})^r$
$S=\sum_{r=1}^{n}\;1-(\large\frac{3}{4})^r$
$=n-\large\frac{\large\frac{3}{4}(1-(\large\frac{3}{4})^n)}{1-\large\frac{3}{4}}$
$=n-3(1-(\large\frac{3}{4})^n)\;.$