Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

# Compute the sum of first n terms of the following series:6 + 66 + 666 + 6666 + ... - Mathematics

Sum

Compute the sum of first n terms of the following series:
6 + 66 + 666 + 6666 + ...

#### Solution

Sn = 6 + 66 + 666 + ...... n terms

= 6[1 + 11 + 111 + ...... n terms]

= 6/9 [9 + 99 + 999 + ..... "n terms"]

= 6/9[(10 - 1) + (10^2 - 1) + (10^3 - 1) + ...  "n terms"]

= 6/9[10 + 10^2 + 10 ^3 .....  "m terms" - (1 + 1 + 1  .... "n terms")]

= 6/9[(10(10^"n" - 1))/(10 - 1) - "n"]

= 6/9((10^"n" - 1)/9 - "n")

= 6/9[(10(10^"n" - 1) - 9"n")/9 - "n"]

= 6/81[10(10^"n" - 1) - 9"n"]

Concept: Finite Series
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 5 Binomial Theorem, Sequences and Series
Exercise 5.3 | Q 3. (ii) | Page 220
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