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Question: If the third term in the binomial expansion of \(6^{8}\) is \((1 + x)^{50},\) , then the rational va...

If the third term in the binomial expansion of 686^{8} is (1+x)50,(1 + x)^{50}, , then the rational value of m is.

A

2

B

2512^{51}

C

3

D

4

Answer

2512^{51}

Explanation

Solution

We have [R]+f−f′=2k\lbrack R\rbrack + f - f^{'} = 2k

By hypothesis, f−f′=2k−[R]⇒f−f′f - f^{'} = 2k - \lbrack R\rbrack \Rightarrow f - f^{'}

⇒ 0≤f<1;0<f′<1⇒−1<f−f′<10 \leq f < 1;0 < f^{'} < 1 \Rightarrow - 1 < f - f' < 1 ⇒ f−f′=0f - f^{'} = 0.