If ∑ k = 1 10 K 2 10 C K 2 = 22000 L , then L is equal to _____.

Step-by-step solution

Given, ∑ K = 1 10   K 2 C K 10 2 = 22000 L Now taking L.H.S we get, ∑ K = 1 10   K 10 C K 2 = ∑ K = 1 10 K × 10 K . C K - 1 9 2 = ∑ K = 1 10 10 . C K - 1 9 2 = 100 ∑ K = 1 10 C K - 1 9 · C 10 - K 9 Now using the rule that ∑ r = 1 n C r - 1 n · C n - r - 1 n = C n 2 n So using the above formula we get, ∑ K = 1 10   K 10 C K 2 = 100 C 9 18 = 100 18 ! 9 ! 9 ! ⇒ 4862000 = 22000 L ⇒ 22000 × 221 = 22000 L Now on comparing we get, Hen