²ⁿC_r = ²ⁿC_r+2 হলে r এর মান কত?

²ⁿC_r = ²ⁿC_r+2
2n!/(r!(2n-r)!) = 2n!/(r+2)! (2n – r -2)!
1/(2n-r)(2n-r-1) = 1/(r+2)(r+1)
r² + 2r + r + 2 = 4n² -2nr – 2nr + r² - 2n + r
2r + 4nr = 4n² - 2n – 2
r(2n + 1) = 2n² - n -1
r(2n + 1) = 2n² - 2n + n -1
r(2n + 1) = (2n+1) (n-1)
r = (n-1)