ⁿC_r+ⁿC_r-1 এর সমান কোনটি?

Explanation:

Another Explanation (5): ⁿC_r+ⁿC_r-1 এর মান নির্ণয়: আমরা জানি, \(^nC_r = \frac{n!}{r!(n-r)!}\) সুতরাং, ⁿC_r+ⁿC_r-1 = \(\frac{n!}{r!(n-r)!} + \frac{n!}{(r-1)!(n-r+1)!}\) = \(\frac{n!}{(r-1)!(n-r)!} [\frac{1}{r} + \frac{1}{n-r+1}]\) = \(\frac{n!}{(r-1)!(n-r)!} [\frac{n-r+1+r}{r(n-r+1)}]\) = \(\frac{n!}{(r-1)!(n-r)!} [\frac{n+1}{r(n-r+1)}]\) = \(\frac{(n+1)n!}{r(r-1)!(n-r+1)(n-r)!}\) = \(\frac{(n+1)!}{r!(n-r+1)!}\) = \(\frac{(n+1)!}{r!((n+1)-r)!}\) = ⁿ⁺¹C_r অতএব, ⁿC_r+ⁿC_r-1 = ⁿ⁺¹C_r 🥳