1/p to the power of left parenthesis n minus m right parenthesis end exponent+1/1 plus p to the power of m minus n right parenthesis end exponent

Asked by apurva151 | 14th Dec, 2015, 05:52: PM

Expert Answer:

begin mathsize 14px style 1 over p to the power of n minus m end exponent plus fraction numerator 1 over denominator 1 plus p to the power of m minus n end exponent end fraction equals fraction numerator 1 plus p to the power of m minus n end exponent plus p to the power of n minus m end exponent over denominator p to the power of n minus m end exponent left parenthesis 1 plus p to the power of m minus n end exponent right parenthesis end fraction equals fraction numerator 1 plus begin display style p to the power of m over p to the power of n end style plus begin display style p to the power of n over p to the power of m end style over denominator begin display style p to the power of n over p to the power of m end style open parentheses 1 plus begin display style p to the power of m over p to the power of n end style close parentheses end fraction equals fraction numerator begin display style fraction numerator p to the power of n p to the power of m plus p to the power of 2 m end exponent plus p to the power of 2 n end exponent over denominator p to the power of n p to the power of m end fraction end style over denominator begin display style p to the power of n over p to the power of m end style plus 1 end fraction equals fraction numerator begin display style fraction numerator p to the power of n p to the power of m plus p to the power of 2 m end exponent plus p to the power of 2 n end exponent over denominator p to the power of n p to the power of m end fraction end style over denominator begin display style fraction numerator p to the power of n plus p to the power of m over denominator p to the power of m end fraction end style end fraction equals fraction numerator p to the power of n p to the power of m plus p to the power of 2 m end exponent plus p to the power of 2 n end exponent over denominator p to the power of n p to the power of m end fraction cross times fraction numerator p to the power of m over denominator p to the power of n plus p to the power of m end fraction equals fraction numerator p to the power of n plus m end exponent plus p to the power of 2 m end exponent plus p to the power of 2 n end exponent over denominator p to the power of n left parenthesis p to the power of n plus p to the power of m right parenthesis end fraction end style

Answered by Rashmi Khot | 15th Dec, 2015, 10:13: AM

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