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CBSE Class 11-science Answered

Ali added the following series if fraction.  How many more fraction in this series he must add to get the answer equal  to onevor more than one 1/2 + 1/4 + 1/8 +1/16 + 1/32 + 1/64
Asked by Nimmi | 17 Feb, 2019, 02:50: PM
answered-by-expert Expert Answer
begin mathsize 16px style 1 half plus 1 fourth plus 1 over 8 plus 1 over 16 plus 1 over 32 plus 1 over 64
straight a equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction comma space straight r equals fraction numerator begin display style 1 fourth end style over denominator begin display style 1 half end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 4 end style end fraction cross times 2 equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction
According space to space the space question comma
straight S subscript straight n space equals 1
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 equals 1
fraction numerator begin display style fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction open parentheses 1 minus open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction close parentheses to the power of straight n close parentheses end style over denominator begin display style 1 minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction end style end fraction equals 1
1 minus open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction close parentheses to the power of straight n equals 1
open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction close parentheses to the power of straight n equals 0
Hence comma space straight n space should space be space infinity space to space get space the space sum space as space 1 space or space more space than space 1.
space
end style
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