Solve this problem please sir 

Asked by sanjaysingh.srct | 6th Aug, 2019, 12:27: AM

Expert Answer:

sum from r equals 0 to infinity of space space sum from s equals 0 to infinity of space space delta subscript r s end subscript space open parentheses 1 half close parentheses to the power of r open parentheses 1 third close parentheses to the power of s
equals sum from r equals 0 to infinity of space space space open parentheses delta subscript r 0 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 0 plus delta subscript r 1 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 1 plus delta subscript r 2 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses squared plus... close parentheses
equals sum from r equals 0 to infinity of space delta subscript r 0 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 0 plus space sum from r equals 0 to infinity of space delta subscript r 1 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 1 plus space sum from r equals 0 to infinity of space delta subscript r 2 end subscript space 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 r open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses squared plus...
equals 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 0 open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 0 plus 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 1 open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses to the power of 1 plus open parentheses fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction close parentheses squared open parentheses fraction numerator begin display style 1 end style over denominator begin display style 3 end style end fraction close parentheses squared plus... space space space space space space space space space space space space space space left parenthesis S i n c e space delta subscript r s end subscript equals 0 space f o r space r not equal to s right parenthesis
equals 1 plus 1 over 6 plus 1 over 6 squared plus....
equals fraction numerator 1 over denominator 1 minus begin display style 1 over 6 end style end fraction equals 6 over 5
p equals 6 comma space q equals 5
rightwards double arrow open vertical bar p squared minus q squared close vertical bar equals open vertical bar 36 minus 25 close vertical bar equals 11

Answered by Renu Varma | 6th Aug, 2019, 10:09: AM

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