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Find the sum to n terms of the sequence, 8, 88, 888, 8888&he...

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Find the sum to n terms of the sequence, 8, 88, 888, 8888…

Answer:

The given sequence is 8, 88, 888, 8888…

This sequence is not a G.P. However, it can be changed to G.P. by writing the terms as

S_n = 8 + 88 + 888 + 8888 + …………….. to n terms

$equals 8 over 9 open square brackets 9 plus 99 plus 999 plus 9999 plus.......... t o space n space t e r m s close square brackets equals 8 over 9 open square brackets open parentheses 10 minus 1 close parentheses plus open parentheses 10 squared minus 1 close parentheses plus open parentheses 10 cubed minus 1 close parentheses plus open parentheses 10 to the power of 4 minus 1 close parentheses plus........ t o to the power of space n space t e r m s close square brackets equals 8 over 9 open square brackets open parentheses 10 plus 10 squared space plus space....... n space t e r m s close parentheses space minus space open parentheses 1 plus 1 plus 1 plus... n space t e r m s close parentheses close square brackets equals 8 over 9 open square brackets fraction numerator 10 open parentheses 10 to the power of n minus 1 close parentheses over denominator 10 minus 1 end fraction space minus space n close square brackets equals 8 over 9 open square brackets fraction numerator 10 open parentheses 10 to the power of n minus 1 close parentheses over denominator 9 end fraction space minus space n close square brackets equals 80 over 81 open parentheses 10 to the power of n minus 1 close parentheses space minus space 8 over 9 n$

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Comments

ayush
2019-03-07 15:42:36

thanks lord

ayush
2019-03-07 15:42:19

thanks lord

ABHISHEK ANAND
2018-03-31 17:26:57

what will be the answer if sum of infinity term are asked.

Sup
2017-02-15 07:35:27

TQ very very much

Amrith
2016-10-04 20:52:22

Thank you very muchðð

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 18: Find the sum to n terms of the sequence, 8, 88, 888, 8888…....

Find the sum to n terms of the | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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