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ICSE Class 10 Answered

Find the common ratio of an infinite G.P. whose each term is ten times the sum of all its succeeding terms 
Asked by 302234926921710 | 22 Jul, 2018, 07:39: PM
answered-by-expert Expert Answer
begin mathsize 16px style Sum space of space infinite space series space is space straight S equals fraction numerator straight a over denominator 1 minus straight r end fraction
now
straight S subscript straight n equals fraction numerator straight a open parentheses 1 minus straight r to the power of straight n close parentheses over denominator 1 minus straight r end fraction
ar to the power of straight n minus 1 end exponent equals 10 open parentheses straight S minus straight S subscript straight n close parentheses..... given
solving
fraction numerator straight r over denominator 1 minus straight r end fraction equals 1 over 10
hence
straight r equals 1 over 11
end style
Answered by Arun | 23 Jul, 2018, 12:00: PM
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