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Question

If the coefficients of $$\displaystyle \left ( 2r+4 \right )^{th},\left ( r-2 \right )^{th}$$ terms in the expansion of $$\displaystyle \left ( 1+x \right )^{18}$$ are equal find r


Solution

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

Mathematics

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