The question is attached above. Please send the step by step complete solution.

Asked by sudhanshubhushanroy | 20th Nov, 2017, 08:12: AM

Expert Answer:

begin mathsize 16px style fraction numerator 1 over denominator straight r open parentheses straight r minus 1 close parentheses open parentheses straight r plus 1 close parentheses end fraction equals fraction numerator straight A over denominator straight r open parentheses straight r minus 1 close parentheses end fraction plus fraction numerator straight B over denominator straight r open parentheses straight r plus 1 close parentheses end fraction
straight A equals bevelled fraction numerator 1 over denominator 2 comma space straight B equals begin display style bevelled fraction numerator negative 1 over denominator 2 end fraction end style end fraction
so comma
sum from straight r equals 2 to straight n of 1 half open parentheses fraction numerator 1 over denominator straight r open parentheses straight r minus 1 close parentheses end fraction minus fraction numerator 1 over denominator straight r open parentheses straight r plus 1 close parentheses end fraction close parentheses
open space the space summation space and space terms space will space get space cancelled end style

Answered by Arun | 29th Nov, 2017, 11:17: AM

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