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Question
Using binomial theorem evaluate .
(ii) (102)5
Solution
(ii) (102)5
\[= (100 + 2 )^5 \]
\[ = ^{5}{}{C}_0 \times {100}^5 \times 2^0 +^{5}{}{C}_1 \times {100}^4 \times 2^1 + ^{5}{}{C}_2 \times {100}^3 \times 2^2 + ^{5}{}{C}_3 \times {100}^2 \times 2^3 +^{5}{}{C}_4 \times {100}^1 \times 2^4 + ^{5}{}{C}_5 \times {100}^0 \times 2^5 \]
\[ = 10000000000 + 1000000000 + 40000000 + 800000 + 8000 + 32\]
\[ = 11040808032\]
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