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 #5
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6 × 6! + 7 × 7! + 8 × 8! + 9 × 9! + 10 × 10! + 11 × 11! + 12 × 12! + 13 × 13! + 14 × 14! = a! - b!

a + b= ?

 

n×n!=(n+11)×n!=[(n+1)1]×n!=(n+1)×n!1×n!=n!×(n+1)n!=(n+1)!n!n×n!=(n+1)!n!

 

6×6!=7!6!7×7!=8!7!8×8!=9!8!9×9!=10!9!10×10!=11!10!11×11!=12!11!12×12!=13!12!13×13!=14!13!14×14!=15!14!sum=7!6!+8!7!+9!8!+10!9!+11!10!+12!11!+13!12!+14!13!+15!14!=7!6!7!+8!+9!8!9!+10!+11!10!11!+12!+13!12!13!+14!+15!14!=15!6!

 

so a = 15 and b = 6

a+b = 15+6 = 21

 

laugh

Oct 10, 2017
 #2
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Oct 10, 2017

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