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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

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
9 years ago
sigma (r=0 to n) (-1)r(5r+3)nCr
=5 sigma(r=0 to n)(-1)rrnCr+3sigma(r=0ton)(-1)rnCr
=5sigma(r=0 to n)(-1)rr.(n/r)n-1Cr-1+3sigma(r=0ton)(-1)rnCr
=5nsigma(r=0 to n) (-1)r n-1Cr-1+3sigma(r=0ton)(-1)rnCr
=5n[ -n-1C0+n-1C1–n-1C2+.........(-1)n n-1Cn-1]+ 3 [nC0-nC1+....+(-1)nnCn]
=5n(0) +3(0)
=0+0
=0
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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