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Home / Doubts and Solutions/JEE/Mathematics

Sir pl tell above question.

Asked by neeraj.unnao 14th March 2017, 6:42 PM
Answered by Expert
Answer:
begin mathsize 16px style 2 to the power of 1 fourth end exponent cross times 4 to the power of 1 over 8 end exponent cross times 8 to the power of 1 over 16 end exponent........ to space infinity equals 2 to the power of 1 fourth end exponent cross times left parenthesis 2 squared right parenthesis to the power of 1 over 8 end exponent cross times left parenthesis 2 cubed right parenthesis to the power of 1 over 16 end exponent........ to space infinity equals 2 to the power of 1 fourth end exponent cross times left parenthesis 2 right parenthesis to the power of 2 over 8 end exponent cross times left parenthesis 2 right parenthesis to the power of 3 over 16 end exponent........ to space infinity equals 2 to the power of open parentheses 1 fourth plus 2 over 8 plus 3 over 16....... to space infinity close parentheses end exponent Let space straight S equals 1 fourth plus 2 over 8 plus 3 over 16....... to space infinity....... left parenthesis ii right parenthesis So comma space 2 to the power of 1 fourth end exponent cross times 4 to the power of 1 over 8 end exponent cross times 8 to the power of 1 over 16 end exponent........ to space infinity equals 2 to the power of straight S space.... left parenthesis asterisk times right parenthesis rightwards double arrow straight S equals 1 fourth plus 2 over 8 plus 3 over 16....... to space infinity rightwards double arrow 1 half straight S equals 1 over 8 plus 2 over 16 plus 3 over 32....... to space infinity space.... left parenthesis iii right parenthesis Substracting space left parenthesis iii right parenthesis space from space left parenthesis ii right parenthesis comma space we space get 1 half straight S equals open parentheses 1 fourth plus 2 over 8 plus 3 over 16....... to space infinity close parentheses minus open parentheses 1 over 8 plus 2 over 16 plus 3 over 32....... to space infinity close parentheses rightwards double arrow 1 half straight S equals 1 fourth plus 2 over 8 minus 1 over 8 plus 3 over 16 minus 2 over 16....... to space infinity rightwards double arrow 1 half straight S equals 1 fourth plus 1 over 8 plus 1 over 16....... to space infinity So comma space this space is space straight a space GP space where space straight a equals 1 fourth comma space straight r equals 1 half less than 1 So comma space 1 half straight S equals fraction numerator 1 fourth over denominator 1 minus 1 half end fraction rightwards double arrow 1 half straight S equals fraction numerator 1 fourth over denominator 1 half end fraction rightwards double arrow straight S equals 1 Substituting space straight S equals 1 space in space left parenthesis asterisk times right parenthesis comma space we space get 2 to the power of 1 fourth end exponent cross times 4 to the power of 1 over 8 end exponent cross times 8 to the power of 1 over 16 end exponent........ to space infinity equals 2 to the power of 1 equals 2 Hence space proved. space end style
Answered by Expert 14th March 2017, 7:43 PM
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