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If ^nC_(r)+^nC_(r+1)=^n+1C_(x), then x=? ( ) A . r B . r-1 C . n D . r+1

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If ^nC_(r)+^nC_(r+1)=^n+1C_(x), then x=? ( ) A . r B . r-1 C . n D . r+1

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ZosiaMaster · Tutor for 5 years

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<div class="c2h-answers"><span class="c2h-answer-order"></span><span class="c2h-answer-content"><span class="c2h-answer">D </span></span><div class="c2h-hint"><span class="c2h-order-label"></span><span class="c2h-detail">use properties<br/>${}^{n}{C}_{r}+{}^{n}{C}_{r-1}={}^{n+1}{C}_{r}$<br/>Replacing $r$ with $r+1,$<br/>$\Rightarrow \; {}^{n}{C}_{r+1}+{}^{n}{C}_{r+1-1}={}^{n+1}{C}_{r+1}$<br/>$\Rightarrow \; {}^{n}{C}_{r+1}+{}^{n}{C}_{r}={}^{n+1}{C}_{r+1}$<br/>it's given $^{n}C_{r}+^{n}C_{r+1}={}^{n+1}C_{x}$<br/>$\Rightarrow \;{}^{n+1}C_{x} = {}^{n+1}{C}_{r+1}$<br/>$\Rightarrow \;x=r+1$</span>
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