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Question
Using binomial theorem, find the value of (1.1)5
Solution
(1.1)5 = (1+ 0.1)5
= 5C0(1)5 + 5C1(1)4 (0.1) + 5C2(1)3 (0.1)2 + 5C3(1)2 (0.1)3 + 5C4(1) (0.1)4 + 5C5(0.1)5
Now, 5C0 = 1 = 5C5
5C1 = 5 = 5C4
5C2 = `(5 xx 4)/(1 xx 2)` = 10 = 5C3
∴ (1.1)5 = 1 + 5 × 1 × 0.1 + 10 × 1 × 0.01 + 10 × 1 × 0.001 + 5 × 1 × 0.0001 + 0.00001
= 1 + 0.5 + 0.1 + 0.01 + 0.0005 + 0.00001
= 1.61051
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