What is the value of the following sum:
1 ! + 2 ! + 3 ! + 4 ! + 5 ! ?
Details and assumptions
The number n ! , read as n factorial , is equal to the product of all positive integers less than or equal to n . For example, 7 ! = 7 × 6 × 5 × 4 × 3 × 2 × 1 .
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First step is to calculate the value of Each Factor, To Sum After them , Thus we have :
1 ! = 1
2 ! = 2 × 1 = 2
3 ! = 3 × 2 × 1 = 6
4 ! = 4 × 3 × 2 × 1 = 2 4
5 ! = 5 × 4 × 3 × 2 × 1 = 1 2 0
For All We sum End Results and found the solution :
1 ! + 2 ! + 3 ! + 4 ! + 5 ! ⇒ 1 + 2 + 6 + 2 4 + 1 2 0 = 1 5 3
Anyone notice this is a narcissistic number? 1^3+5^3+3^3=153
( 1 ) + ( 2 ∗ 1 ) + ( 3 ∗ 2 ∗ 1 ) + ( 4 ∗ 3 ∗ 2 ∗ 1 ) + ( 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 ) 1 + 2 + 6 + 2 4 + 1 2 0 = 1 5 3
1 ! + 2 ! + 3 ! + 4 ! + 5 !
Just putting the value of the factorials
⟹ 1 + 2 + 6 + 2 4 + 1 2 0
⟹ 1 5 3
Find the factorials of each number and add them together: 1- 1 (no other numbers) 2- 2x1=2 3- 3x2x1=6 4- 4x3x2x1=24 5- 5x4x3x2x1=120
1+2+6+24+120=153
Read the Details and assumptions for the solution on getting the factorials.
1! = 1 2! = 2X1 = 2 3! = 3X2X1 = 6 4! = 4x3x2x1 = 24 5! = 5x4x3x2x1 = 120
1+2+6+24+120 = 153
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1!+2!+3!+4!+5! =1+2+6+24+120 =153