The sum of the series ∑r=0n (−1)r  nCr12r+3r22r+7r23r+15r24r+…+m terms  is  

The sum of the series r=0n(1)r  nCr12r+3r22r+7r23r+15r24r++m terms  is 

 

  1. A

    2mn12mn2n1

  2. B

    2mn12n1

  3. C

    2mn+12n+1

  4. D

    None of these

    Register to Get Free Mock Test and Study Material

    +91

    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    nn(1)rnCr12r+3r22r+7r23r+ upto m terms 

    =r=0n(1)r nCr12r+r=0n(1)rnCr3r22r+r=0n(1)rnCr7r23r+

    =112n+134n+178n+up to M terms

    =12n+122n+123n upto m terms 

    =12n112nm112n=2mn12mn2n1

    Chat on WhatsApp Call Infinity Learn

      Register to Get Free Mock Test and Study Material

      +91

      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.