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avatar+214 

 

Find the sum 1/2!+2/3!+3/4!+...+(n−1)/n!. Express your answer in terms of n.

 #1
avatar+128794 
+1

1/2 +  1/3  +  1/8  +  1/30  +   1/144  + 1/840 +  ........

 

Progressive sums

 

5/6,   23/24,   119/120,    719 / 720,    5039 / 5040    + ......  =  (n! - 1) /n!  =    n! / n !  +  1 / n!

 

Note that   n! / n!   = 1     (for  integer n   ≥ 3)

 

And as n gets very large, 1 / n!  ≈  0

 

So....the sum  =   1

 

 

 

cool cool cool

 Apr 7, 2024
 #2
avatar+214 
+1

Thannks so much!smiley

 #3
avatar+214 
+1

I don't think the answer is rightcrying

Do you think you might of did something wrong?

 #4
avatar+128794 
+1

 

 

cool cool cool

.
 Apr 7, 2024

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