The number of integral terms in the expansion of $ \left( {5^\frac{1}{2}} + 7^\frac{1}{8} \right)^{1016} $ is:
Solution
<p>$$\begin{aligned}
&\begin{aligned}
& \mathrm{T}_{\mathrm{r}}={ }^{1016} \mathrm{C}_{\mathrm{r}}(5)^{\frac{1016-\mathrm{r}}{2}} 7^{\frac{\mathrm{r}}{8}} \\
& \Rightarrow \mathrm{r}=0,8,16,24, \ldots ., 1016 \\
& 1016=0+(\mathrm{n}-1) 8 \\
& \Rightarrow \mathrm{n}-1=\frac{1016}{8}=127
\end{aligned}\\
&\text { So, } \mathrm{n}=128 \text {. }
\end{aligned}$$</p>
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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