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Home / Doubts and Solutions/JEE/Mathematics

ques no 6

Asked by chandanbr6004 15th November 2017, 9:42 PM
Answered by Expert
Answer:
begin mathsize 16px style sum from straight r equals 1 to 100 of open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses cubed minus stack 3 sum with straight r equals 1 below and 100 on top open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses plus 1 equals sum from straight r equals 1 to 100 of open parentheses 2 to the power of straight r plus 2 to the power of negative straight r end exponent plus 3 open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses close parentheses minus stack 3 sum with straight r equals 1 below and 100 on top open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses plus 1 equals sum from straight r equals 1 to 100 of open parentheses 2 to the power of straight r plus 2 to the power of negative straight r end exponent close parentheses plus 3 sum from straight r equals 1 to 100 of open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses minus stack 3 sum with straight r equals 1 below and 100 on top open parentheses 2 to the power of straight r divided by 3 end exponent plus 2 to the power of bevelled fraction numerator negative straight r over denominator 3 end fraction end exponent close parentheses plus 1 equals sum from straight r equals 1 to 100 of open parentheses 2 to the power of straight r plus 2 to the power of negative straight r end exponent close parentheses plus 1 equals open square brackets open parentheses 2 to the power of 1 plus 2 squared plus 2 cubed plus.... plus 2 to the power of 100 close parentheses plus open parentheses 2 to the power of negative 1 end exponent plus 2 to the power of negative 2 end exponent plus 2 to the power of negative 3 end exponent plus.... plus 2 to the power of negative 100 end exponent close parentheses close square brackets plus 1 equals open parentheses fraction numerator 2 open parentheses 2 to the power of 100 minus 1 close parentheses over denominator 2 minus 1 end fraction plus fraction numerator 2 to the power of negative 1 end exponent open parentheses 1 minus 2 to the power of negative 100 end exponent close parentheses over denominator 2 to the power of negative 1 end exponent end fraction close parentheses plus 1 equals fraction numerator 2 to the power of 201 minus 1 over denominator 2 to the power of 100 end fraction end style
Answered by Expert 7th December 2017, 2:16 PM
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