Let S be the sum, P the product and R th | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn

Answer:

Let the G.P. be a, ar, ar2, ar3, … arn – 1…

According to the given information,

S space equals space fraction numerator a space open parentheses r to the power of n space minus 1 close parentheses over denominator r space minus 1 end fraction P space equals space a to the power of n space end exponent cross times space r to the power of 1 plus 2 plus... plus n minus 1 end exponent space space space space equals space a to the power of n space end exponent r to the power of fraction numerator n open parentheses n minus 1 close parentheses over denominator 2 end fraction space space space space space space space open square brackets because space S u m space o f space f i r s t space n space n a t u r a l space n u m b e r s space i s space fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 end fraction close square brackets end exponent R space equals space 1 over a space plus space fraction numerator 1 over denominator a r end fraction space plus space... space plus space fraction numerator 1 over denominator a r to the power of n minus 1 end exponent end fraction space space space space equals space fraction numerator r to the power of n minus 1 end exponent plus r to the power of n minus 2 end exponent space plus space... r plus 1 over denominator a r to the power of n minus 1 end exponent end fraction space space space space equals space fraction numerator 1 open parentheses r to the power of n space minus 1 close parentheses over denominator open parentheses r minus 1 close parentheses end fraction space cross times space fraction numerator 1 over denominator a r to the power of n minus 1 end exponent end fraction space space space space space space space space space space open square brackets because space 1 comma r comma... r to the power of n minus 1 end exponent space f o r m s space a space G. P. close square brackets space space space space equals space fraction numerator r to the power of n space minus 1 over denominator a r to the power of n minus 1 end exponent open parentheses r minus 1 close parentheses end fraction therefore space P squared R to the power of n space equals space a to the power of 2 n end exponent r to the power of n open parentheses n minus 1 close parentheses space end exponent fraction numerator open parentheses r to the power of n space minus 1 close parentheses to the power of n over denominator a to the power of n r to the power of n open parentheses n minus 1 close parentheses end exponent open parentheses r minus 1 close parentheses to the power of n end fraction space space space space space space space space space space space space space space space space space equals space fraction numerator a to the power of n open parentheses r to the power of n minus 1 close parentheses to the power of n over denominator open parentheses r minus 1 close parentheses to the power of n end fraction space space space space space space space space space space space space space space space space space equals space open square brackets fraction numerator a open parentheses r to the power of n space minus 1 close parentheses over denominator open parentheses r minus 1 close parentheses end fraction close square brackets to the power of n space space space space space space space space space space space space space space space space equals space S to the power of n

Hence P2 Rn= Sn


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Comments

  • Kunal
  • 2019-02-01 08:51:31

Thanx....🙂

  • Adi
  • 2018-12-24 08:31:22

Ty

  • Anjali
  • 2018-10-18 09:32:23

Thanks for the solution

  • Nitesh
  • 2018-09-11 12:40:59

Not satisfied

  • Vishu
  • 2018-08-04 15:47:39

Nice

  • Sweety
  • 2018-04-06 13:01:43

P^2 = (S/R)^n

  • frankestine
  • 2017-03-23 21:33:23

the answer is not easy to understand

  • Evam Spy
  • 2017-02-21 00:53:01

The color of the page is very uncomfortable to the eyes

  • Dibyashree Bagchi
  • 2017-01-17 12:49:58

Thank you so much...

  • Sudhanshu
  • 2016-12-15 04:36:06

I have better solution than yours

Comment(s) on this Question

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 5 , Question 14: Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove th....

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