JEE MAIN - Mathematics (2020 - 3rd September Morning Slot - No. 8)
The value of (2.1P0
– 3.2P1 + 4.3P2 .... up to
51th term)
+ (1! – 2! + 3! – ..... up to 51th term) is equal to :
+ (1! – 2! + 3! – ..... up to 51th term) is equal to :
1
1 + (51)!
1 – 51(51)!
1 + (52)!
Explanation
(2.1P0
– 3.2P1 + 4.3P2 .... up to
51th term)
+ (1! – 2! + 3! – ..... up to 51th term)
= ( 2.1! - 3.2! + 4.3! - ....+ 52.51!)
+ ( 1! – 2! + 3! – ..... + (51)! )
= (2! - 3! + 4! .....+ 52! )
+ ( 1! - 2! + 3! - 4! + .....+ 51! )
= 1 + (52)!
+ (1! – 2! + 3! – ..... up to 51th term)
= ( 2.1! - 3.2! + 4.3! - ....+ 52.51!)
+ ( 1! – 2! + 3! – ..... + (51)! )
= (2! - 3! + 4! .....+ 52! )
+ ( 1! - 2! + 3! - 4! + .....+ 51! )
= 1 + (52)!
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