Find an approximation of (0.99)5 using the first three terms of its expansion.
(0.99)5 = (1 - 0.01)5
We know that-
Hence
= a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5
Thus, (a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5
Putting a = 1 & b = -0.01, we get-
(1 + (-0.01))5 = (1)5 + 5(1)4(-0.01) + 10(1)3(-0.01)2 + 10(1)2(-0.01)3 + 5(1)(-0.01)4 + (-0.01)5
Using first three terms,
(0.99)5 = (1)5 + 5(1)4(-0.01) + 10(1)3(-0.01)2
= 1 - 0.05 + 0.001
= 1.001 - 0.050
= 0.951
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