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  4. The value of (4 ⋅ n C1+4 ⋅ n C2+42 ⋅ n C3+ ldots ldots+4n-1) is

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Q. The value of $\left(4 \cdot{ }^n C_1+4 \cdot{ }^n C_2+4^2 \cdot{ }^n C_3+\ldots \ldots+4^{n-1}\right)$ is

Binomial Theorem

Solution:

$\text { Given } E =4 \cdot{ }^{ n } C _1+4^2 \cdot{ }^{ n } C _2+4^3 \cdot{ }^{ n } C _3+\ldots \ldots .+4^{ n } \cdot{ }^{ n } C _{ n } $
$=(1+4)^n-1 \Rightarrow 5^n-1 \Rightarrow D$