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Binomial Expression

Find the valu...

Question

Find the value of r if the coefficient of ${(2 r + 2)}^{t h}$ and ${(r + 1)}^{t h}$ terms are in the expansion of ${(1 + x)}^{43}$ are equal.

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Solution

$(1 + x)^{43} \Rightarrow T_{2 r + 2} =^{43} C_{2 r + 1} (1) x^{2 r + 1}$
$T_{r + 1} =^{43} C_{r} (1) x^{r}$
$2 r + 1 + r = 43$
$2 r = 42$
$r = 14$
$42 r + 1 = r$
$r = 1$

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