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Question
Using binomial theorem, find the value of (0.9)4
Solution
(0.9)4 = (1 – 0.1)4
= 4C0(1)4 – 4C1(1)3(0.1) + 4C2(1)2(0.1)2 – 4C3(1)(0.1)3 + 4C4(0.1)4
Now, 4C0 = 1 = 4C4
4C1 = 4 = 4C3
4C2 = `(4 xx 3)/(1 xx 2)` = 6
∴ (0.9)4 = 1 × 1 – 4 × 1 × 0.1 + 6 × 1 × 0.01 – 4 × 1 × 0.001 + 1 × 0.0001
= 1 – 0.4 + 0.06 – 0.004 + 0.0001
= 1.0601 – 0.404
= 0.6561
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