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Binomial Theorem — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBinomial Theorem1 Mark
Question
Write the expression ${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$in the simplest form.
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Answer

${^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r-1}}+2\times{^\text{n}}\text{C}_{\text{r}-1}$ $=({^\text{n}}\text{C}_{\text{r}+1}+{^\text{n}}\text{C}_{\text{r}})+​​​​{^\text{n}}\text{C}_{\text{r}}+​​​​{^\text{n}}\text{C}_{\text{r-1}}$ $={^\text{n+1}}\text{C}_{\text{r}+1}+{^\text{n+1}}\text{C}_{\text{r}}$ $={^\text{n+1+1}}\text{C}_{\text{r}+1}$ $={^\text{n+2}}\text{C}_{\text{r}+1}$

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