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Binomial Theorem — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem2 Marks
Question
Using binomial theorem, evaluate: (99)5
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Answer

(99)5 = (100 - 1)5
Using binomial theorem, we have
$(100 - 1){ = ^5}{C_0}{(100)^5}{ + ^5}{C_1}{(100)^4}( - 1)$${ + ^5}{C_2}{(100)^3}{( - 1)^2}{ + ^5}{C_3}{(100)^2}{( - 1)^3}$
${ + ^5}{C_4}(100){(1)^4}{ + ^5}{C_5}{( - 1)^5}$
= (100)5 + 5(100)4(-1) + 10(100)3 + 10(100)2(-1)3 + 5(100) + (-1)5
= 10000000000 - 500000000 + 10000000 - 100000 + 500 - 1
= 10010000500 - 500100001
= 9509900499

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