Q9 of 25 Page 8

Using binomial theorem, evaluate each of the following (99)5


(99)5 = (100- 1)5
            = 5C0(100)5 - 5C1(100)4.1 + 5C2(100)3.(1)2 - 5C3(100)2.(1)2 + 5C4(100)1(1)4 - 5C5(1)5
            = (100)5 – 5 × (100)4 + 10 ×(100)3 – 10 × (100)2 + 5 × 100 – 1
            = 10000000000-500000000+ 10000000 - 100000 + 500 - 1
            = 10010000500 - 500100001
            = 9509900499

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