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Question Number 63940 by gunawan last updated on 11/Jul/19

$$\mathrm{If}\mathrm{the}\mathrm{coefficient}\mathrm{of}(2r+4)\mathrm{th}\mathrm{and}(r-2)\mathrm{th}$$$$\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}{(1+x)}^{18}\mathrm{are}$$$$\mathrm{equal},\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}r\mathrm{is}$$

Answered by mr W last updated on 11/Jul/19

$$coef.ofk+1thtermis$$$$C_k^{18}=C_{18-k}^{18}$$$$(2r+4-1)+(r-2-1)=18$$$$\Rightarrow r=6$$

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