Using the Binomial Theorem,evaluate (101)^{4} | vedclass

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(A) We can express $101$ as $(100 + 1)$.Using the Binomial Theorem,$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$.Here,$a = 100$,$b = 1$,and $n

Vedclass · Accepted Answer

$104060401$

Vedclass · Answer

(A) We can express $101$ as $(100 + 1)$.Using the Binomial Theorem,$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$.Here,$a = 100$,$b = 1$,and $n = 4$.$(100 + 1)^4 = \binom{4}{0}(100)^4 + \binom{4}{1}(100)^3(1) + \binom{4}{2}(100)^2(1)^2 + \binom{4}{3}(100)(1)^3 + \binom{4}{4}(1)^4$$= 1 	imes 100000000 + 4 	imes 1000000 + 6 	imes 10000 + 4 	imes 100 + 1$$= 100000000 + 4000000 + 60000 + 400 + 1$$= 104060401$

Using the Binomial Theorem,evaluate $(101)^{4}$.

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