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Question
Using binomial theorem, evaluate the following:
(99)5
Solution
99 can be written as the sum or difference of two numbers whose powers are easier to calculate and then, Binomial Theorem can be applied.
It can be written that, 99 = 100 – 1
∴ `(99)^5 = (100 - 1)^5`
= `""^5C_0 (100)^5 + ^5C_1 xx (100)^4 xx (- 1) + ^5C_2 xx (100)^3 xx (- 1)^2 + ^5C_3 xx (100)^2 xx (- 1)^3 + ^5C_4 xx (100) xx (-4)^4 + (-1)^5`
= 10000000000 – 5 x 100000000 + 10 x 1000000 – 10 x 10000 + 5 x 100 – 1
= 10000000000 – 500000000 + 10000000 – 100000 + 500 – 1
= 9509900499
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