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Middle Terms

If the coeffi...

Question

If the coefficients of ${(2 r + 4)}^{t h}, {(r - 2)}^{t h}$ terms in the expansion of ${(1 + x)}^{18}$ are equal find r

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Solution

Hence
$^{18} C_{2 r + 3} =^{18} C_{r - 3}$
Therefore
$18 - (2 r + 3) = r - 3$
$\Rightarrow 15 - 2 r = r - 3$
$\Rightarrow 18 = 3 r$
$\Rightarrow r = 6$

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