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  4. If (1+b y)n=(1+8 y+24 y2+ ldots.) where n ∈ N then the value of b and n are respectively-

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Q. If $(1+b y)^n=\left(1+8 y+24 y^2+\ldots.\right)$ where $n \in N$ then the value of $b$ and $n$ are respectively-

Binomial Theorem

Solution:

$(1+b y)^n=1+8 y+24 y^2+$
$(1+b y)^n=1+n \cdot b y+\frac{n(n-1)}{2} \cdot b^2 y^2+\ldots \ldots \ldots$
by comparison
$bn =8.....$(1)
$\frac{n(n-1)}{2} b^2=24.....$(2)
$4 n-4=3 n$
$n =4$
and $ b=2$