Many Facts!

What is the value of the following sum:

1 ! + 2 ! + 3 ! + 4 ! + 5 ! ? 1! + 2! + 3! + 4! + 5! ?

Details and assumptions

The number n ! n! , read as n factorial , is equal to the product of all positive integers less than or equal to n n . For example, 7 ! = 7 × 6 × 5 × 4 × 3 × 2 × 1 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 .


The answer is 153.

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8 solutions

Valian Fil Ahli
Oct 26, 2013

1!+2!+3!+4!+5! =1+2+6+24+120 =153

Gabriel Merces
Oct 21, 2013

First step is to calculate the value of Each Factor, To Sum After them , Thus we have :

1 ! 1! = = 1 1

2 ! 2! = = 2 × 1 2 \times 1 = = 2 2

3 ! 3! = = 3 × 2 × 1 3 \times 2 \times 1 = = 6 6

4 ! 4! = = 4 × 3 × 2 × 1 4 \times 3 \times 2 \times 1 = = 24 24

5 ! 5! = = 5 × 4 × 3 × 2 × 1 5 \times 4 \times 3 \times 2 \times 1 = = 120 120

For All We sum End Results and found the solution :

1 ! 1! + + 2 ! 2! + + 3 ! 3! + + 4 ! 4! + + 5 ! 5! \Rightarrow 1 1 + + 2 2 + + 6 6 + + 24 24 + + 120 120 = = 153 \boxed{153}

David Holcer
Mar 23, 2015

Anyone notice this is a narcissistic number? 1^3+5^3+3^3=153

Patrick Feltes
Mar 28, 2014

( 1 ) + ( 2 1 ) + ( 3 2 1 ) + ( 4 3 2 1 ) + ( 5 4 3 2 1 ) 1 + 2 + 6 + 24 + 120 = 153 (1) + (2 * 1) + (3 * 2 * 1) + (4 * 3 * 2 * 1) + (5 * 4 * 3 * 2 * 1) \\1 + 2 + 6 + 24 + 120 = 153

Iranna Hubballi
Mar 9, 2014

1+2+6+24+120=153

Ayon Pal
Oct 23, 2013

1 ! + 2 ! + 3 ! + 4 ! + 5 ! 1! + 2! + 3! + 4! + 5!

Just putting the value of the factorials

1 + 2 + 6 + 24 + 120 \implies 1 + 2 + 6 + 24 + 120

153 \implies 153

Joshua Wardle
Oct 22, 2013

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.

Johan Bama
Oct 22, 2013

1! = 1 2! = 2X1 = 2 3! = 3X2X1 = 6 4! = 4x3x2x1 = 24 5! = 5x4x3x2x1 = 120

1+2+6+24+120 = 153

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