InterviewSolution
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InterviewSolution
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Evaluate the following using binomial theorem: (i) (101)4 (ii) (999)5 |
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Answer» (i) (x + a)n = nC0 xna0 + nC1 xn-1 a1 + nC2 xn-2 a2 + … + nCrxn-r ar + … + nCn an (101)4 = (100 + 1)4 = 4C0 (100)4 + 4C1 (100)3 (1)1 + 4C2 (100)2 (1)2 + 4C3 (100)1 (1)3 + 4C4 (1)4 = 1 x (100000000) + 4 x (1000000) + 6 x (10000) + 4 x 100 + 1 x 1 = 100000000 + 4000000 + 60000 + 400 + 1 = 10,40,60,401 (ii) (x + a)n = nC0 xna0 + nC1 xn-1 a1 + nC2 xn-2 a2 + … + nCrxn-r ar + … + nCn an (999)5 = (1000 – 1)5 = 5C0 (1000)5 – 5C1 (1000)4 (1)1 + 5C2 (1000)3 (1)2 – 5C3 (1000)2 (1)3 + 5C4 (1000) (1)4 – 5C5 (1)5 = 1(1000)5 – 5(1000)4 – 10(1000)3 – 10(1000)2 + 5(1000) – 1 = 1000000000000000 – 5000000000000 + 10000000000 – 10000000 + 5000 – 1 = 995009990004999 |
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