JEE Main202126 Aug 2021Morning ShiftMathematicsSequences and SeriesActual
If P 1 1 + 2 · P 2 2 + 3 · P 3 3 + … + 15 · P 15 15 = P r q - s , 0 ≤ s ≤ 1 , then C r - s q + s is equal to
Correct answer
0
Step-by-step solution
We have, P 1 1 + 2 · P 2 2 + 3 · P 3 3 + … + 15 · P 15 15 = P r q - s where, 0 ≤ s ≤ 1 Now, 1 P 1 + 2 · 2 P 2 + 3 ⋅ 3 P 3 + … + 15 · 15 P 15 = 1 ! + 2 · 2 ! + 3 · 3 ! + … … + 15 · 15 ! = ( 2 ! - 1 ! ) + ( 3 ! - 2 ! ) + ( 4 ! - 3 ! ) + … … + ( 16 ! - 15 ! ) ∵ n · n ! = n + 1 - 1 n ! = n + 1 ! - n ! = 16 ! − 1 ! = P r q − s ⇒ q = r = 16   &   s = 1 So, C r - s q + s = C 15 17 = 17 &