Title Maths XII - Binomial theorem - Binomial coeffficients .ppt.ppt ✅

BINOMIAL COEFFICIENTS
BINOMIAL COEFFICIENTS
Theorem : If cr denotes ncr then i) C0 +C1 +C2 + …..+Cn = 2n ii) C0 +C2 +C4+…… = C1 +C3 +C5 + ….= 2n-1 Proof We know that (1 + x)n = C0 + C1 x + C2 x2 + …. + Cn xn →(1) Take x = 1 in (1), Take x = – 1 in (1), We get we get 2n= C0 + C1 + C2 + ….+ Cn →(2) 0 = C0 – C1 + C2 – C3…+ (-1)n Cn → (3)