Question

JEE Mains Maths question is in the image

Answer 1

it has given that S = (2 ¹P₀ - 3²P₁ + 4 ³P₂ + .... + 51 terms) + (1 ! - 2 ! + 3! - 4 ! + ...... + 51 terms)

We have to find the value of S.

solution : we know, $^nP_r$ = n !/(n - r)!

so, ¹P₀ = 1!/(1 - 0)! = 1

²P₁ = 2!/(2 - 1)! = 2!

³P₂ = 3!/(3 - 2)! = 3!

...........

..... ....

⁵¹P₅₀ = 51!/(51 - 50)! = 51!

now S = (2 × 1 ! - 3 × 2! + 4 × 3 ! - 5 × 4! + .... + 52 × 5!) + (1 ! - 2! + 3! - 4! + ..... + 51 !)

= (2! - 3! + 4! - 5! + .... + 52 !) + (1 ! - 2! + 3! - 4! + ..... + 51 !)

= 1 + 52!

Therefore the value of S will be (1 + 52 !)

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