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Question Number 157230 by Jamshidbek last updated on 21/Oct/21

$${(3\mathrm{x}+1)}^{100}$$$$\mathrm{Find}\mathrm{this}\max \mathrm{Koeffitcient}$$

Answered by mr W last updated on 21/Oct/21

$$a_n=3^n{C}_n^{100}$$$$a_{n+1}=3^{n+1}{C}_{n+1}^{100}$$$$\frac{a_{n+1}}{a_n}=\frac{3C_{n+1}^{100}}{C_n^{100}}=\frac{3(100-n)}{(n+1)}<1$$$$299<4n$$$$n>\frac{299}{4}\Rightarrow n⩾75$$$$maximumisatn=75$$$$max=a_{75}=3^{75}{C}_{75}^{100}$$

Commented by Tawa11 last updated on 21/Oct/21

$$\mathrm{Great}\mathrm{sir}$$

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