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State and prove Binomial theorem for positive integral index ‘n’. |
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Answer» Statement: “If ‘n’ is a +ve integer then (x + a)n = nc0 xn a0 + nc1 xn-1 a1+ n2 xn-2 .a2 + ………….. + ncn x0 an. Proof : (By Mathematical induction): Let p(n) : (x + a)n = nc0 x na0 + nc1 xn-1 a1 + nC2 xn-2 a2 + ……………… + ncn x0an . Step1 : Prove that P(1) is true when n= 1, L.H.S = (x + a)1 = x + a; RHS = 1c0 x1 a1 = |x.| + 1.1.a = x + a L.H.S. = R.H.S. ∴ P(1) is true |
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