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Binomial Theorem — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem2 Marks
Question
Prove that ${\sum\limits_{r=0}^n3^r\;^nC_r=4^n}$
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Answer

$\sum_{r=0}^n{ }^n C_r a^{n-r} b^r=(a+b)^n \ldots \ldots \ldots \text { (1) } $
$\text { Now, } \sum_{r=0}^n 3^{r n} C_r=\sum_{r=0}^n{ }^n C_r(1)^{n-r} \cdot 3^r=(1+3)^n$
$\quad=4^n$

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