8. Sequences and Series
easy

गुणोत्तर श्रेणी का योगफल निर्दिष्ट पदों तक ज्ञात कीजिए।

$0.15,0.015,0.0015, \ldots 20$ पदों तक

A

$\frac{1}{6}\left[1-(0.1)^{20}\right]$

B

$\frac{1}{6}\left[1-(0.1)^{20}\right]$

C

$\frac{1}{6}\left[1-(0.1)^{20}\right]$

D

$\frac{1}{6}\left[1-(0.1)^{20}\right]$

Solution

The given $G.P.$ is $0.15,0.015,0.00015 \ldots$

Here, $a=0.15$ and $r=\frac{0.015}{0.15}=0.1$

$S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$

$\therefore S_{20}=\frac{0.15\left[1-(0.1)^{20}\right]}{1-0.1}$

$=\frac{0.15}{0.9}\left[1-(0.1)^{20}\right]$

$=\frac{15}{90}\left[1-(0.1)^{20}\right]$

$=\frac{1}{6}\left[1-(0.1)^{20}\right]$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.