Tamil Nadu Board of Secondary EducationHSC Arts Class 11th

Compute the sum of first n terms of the following series:8 + 88 + 888 + 8888 + ... - Mathematics

Sum

Compute the sum of first n terms of the following series:
8 + 88 + 888 + 8888 + ...

Solution

Sn = 8 + 88 + 888 + 8888 + ...... n terms

= 8[1 + 11 + 1111 + ...... n terms]

= 8/9 [9 + 99 + 999 + ..... "n terms"]

= 8/9[(10 - 1) + (10^2 - 1) + (10^3 - 1) + ...  "n terms"]

= 8/9[10 + 10^2 + ...  "m terms" - (1 + 1 + 1 .... "n terms")]

= 8/9[(10(10^"n" - 1))/(10 - 1) - "n"]

= 8/9[(10(10^"n" - 1))/9 - "n"]

= 80/81(10^"n" - 1) - (8"n")/9

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. (i) | Page 220
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