ⁿC_r +ⁿC_r–1=?

Explanation:

Another Explanation (5): আমরা জানি, ⁿC_r = \( \frac{n!}{r!(n-r)!} \) তাহলে, ⁿC_r + ⁿC_r–1 = \( \frac{n!}{r!(n-r)!} + \frac{n!}{(r-1)!(n-r+1)!} \) = \( \frac{n!}{(r-1)!(n-r)!} [\frac{1}{r} + \frac{1}{n-r+1}] \) 🤔 = \( \frac{n!}{(r-1)!(n-r)!} [\frac{n-r+1+r}{r(n-r+1)}] \) 🤓 = \( \frac{n!}{(r-1)!(n-r)!} [\frac{n+1}{r(n-r+1)}] \) 🤯 = \( \frac{(n+1)!}{r!(n-r+1)!} \) 🎉 = ⁿ⁺¹C_r 😎 অতএব, ⁿC_r + ⁿC_r–1 = ⁿ⁺¹C_r 🥳