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Prove that: 3C0-8C1+13C2-18C3 +…. upto n+1 terms = 0

Prove that: 3C0-8C1+13C2-18C3 +…. upto n+1 terms = 0

Grade:12

3 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
sigma(r=0 to n) (-1)^r (5r+1)Cr
=5sigma(-1)^rCr+sigm(-1)^rCr
=5sigma(-1)^r.r.(n/r).(n-1)Cr+sigm(-1)^r.Cr
=5nsigma(-1)^r.(n-1)Cr+sigma(-1)^rCr
=5n(0)+0
=0
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

Pushkar Aditya
71 Points
7 years ago
Hello, Rinkoo Gupta I would really appreciate that you have replied so soon. But could you please explain me how sigma(-1)^r Cr = 0 How ? As far as I know.. Sigma Cr is equal to 2^n. Thanks Siddharth Singh
Siddharth Singh
22 Points
7 years ago
Hello, Thank you for answering so soon. I really appreciate that.. But I would like to ask you.. How Sigma(-1)^r Cr=0

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