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ICSE Class 10 Answered

Sum of n terms of the series  0.8+0.88+0.888 ............n terms
Asked by Sabitamishra943 | 16 Feb, 2019, 05:45: AM
answered-by-expert Expert Answer
S = 0.8+0.88+0.888...................to n terms
 
S = 8×[0.1 + 0.11 + 0.111 ............................to n terms ]
 
begin mathsize 16px style S space equals space 8 cross times open square brackets 1 over 10 space plus space 11 over 100 space plus space 111 over 1000 space........................... t o space n space t e r m s close square brackets S space equals space 8 cross times open square brackets space open parentheses 1 over 10 plus 1 over 100 plus 1 over 1000................. t o space n space t e r m s close parentheses space space plus space open parentheses 10 over 100 plus 100 over 1000............ t o space left parenthesis n minus 1 right parenthesis space t e r m s close parentheses close square brackets s space equals space 8 cross times open square brackets 1 over 10 space cross times space fraction numerator 1 minus open parentheses begin display style 1 over 10 end style close parentheses to the power of n over denominator 1 minus begin display style 1 over 10 end style end fraction space space space plus space fraction numerator n minus 1 over denominator 10 end fraction close square brackets space space equals space 8 cross times open square brackets 1 over 9 open parentheses 1 minus open parentheses 1 over 10 close parentheses to the power of n close parentheses space plus space fraction numerator open parentheses n minus 1 close parentheses over denominator 10 end fraction space close square brackets end style
Answered by Thiyagarajan K | 16 Feb, 2019, 02:02: PM

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