If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?
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Hi Mate!!!
15! - 14! - 13! = { 13! × 14 × 15 - 13! × 14 - 13! }
=>. 13! { 14 × 15 - 14 - 1 }
=>. 13! { 195 }
15! - 14! - 13! = { 13! × 14 × 15 - 13! × 14 - 13! }
=>. 13! { 14 × 15 - 14 - 1 }
=>. 13! { 195 }
Answered by
0
Given:
(1 × 2 × 3 × 4 ........ × n) = n!
where n! means "n factorial"
Find:
The value of 15! - 14! - 13!.
Solution:
15! - 14! - 13! = (15 x 14!) - (14 x 13!) - 13!
= (15 x 14 x 13!) - (14 x 13!) - 13!
= 13! [ (15 x 14) - 14 - 1]
= 13! [210 - 14 -1]
= 13! x 195
= 6227020800 x 195
= 1,214,269,056,000
Hence, the value of 15! - 14! - 13! = 13! x 195 = 1,214,269,056,000
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