Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the sum of the following series up to n terms: .6 +. 66 +. 666+…

21(ii)   Find the sum of the following series up to n terms: 

               .6 +. 66 +. 666+…

Answers (1)

best_answer

Sum of  0.6 +0. 66 + 0. 666+….................

It can be written  as 

S_n=0.6+0.66+0.666+.......................... to n terms

S_n=6[0.1+0.11+0.111+0.1111+................]

S_n=\frac{6}{9}[0.9+0.99+0.999+0.9999+................]

S_n=\frac{6}{9}[(1-\frac{1}{10})+(1-\frac{1}{10^2})+(1-\frac{1}{10^3})+(1-\frac{1}{10^4})+................]

S_n=\frac{2}{3}[(1+1+1.....................n\, terms)-\frac{1}{10}(1+\frac{1}{10}+\frac{1}{10^2}+...................n \, terms)]

S_n=\frac{2}{3}[n-\frac{\frac{1}{10}(\frac{1}{10}^n-1)}{\frac{1}{10}-1}]

S_n=\frac{2n}{3}-\frac{2}{30}[\frac{10(1-10^-^n)}{9}]

S_n=\frac{2n}{3}-\frac{2}{27}(1-10^-^n)

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE 12th Result 2026 Date: Here’s what previous years’ trends indicate
anam-khan

CBSE Class 12th marks uploading for schools in West Asia starts from April 8
anam-khan

CBSE question papers QR codes part of 'internal systems'; board cautions 'unverified claims'

Latest Question