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# PS - sum of factorials

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Manager
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PS - sum of factorials [#permalink]

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28 Apr 2007, 05:08
What is 1!+2!+...+20! ?

Do you guys know any trick to make such a calculation?

Thanks!
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Re: PS - sum of factorials [#permalink]

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28 Apr 2007, 05:36
querio wrote:
What is 1!+2!+...+20! ?

Do you guys know any trick to make such a calculation?

Thanks!

i am not aware of any nice shortcut. however, sometime the answer choices help in that given these you can find the right answer quickly. for example the units digit of the answer can be quickly calculated (it is 3), so if you had 5 answer choices and only one of those had 3 in its unit digit - you could have your answer very quickly.
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Re: PS - sum of factorials [#permalink]

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28 Apr 2007, 06:09
I would interested to see a shortcut too..

btw Hobbit, how did you figure unit digit was 3?

hobbit wrote:
querio wrote:
What is 1!+2!+...+20! ?

Do you guys know any trick to make such a calculation?

Thanks!

i am not aware of any nice shortcut. however, sometime the answer choices help in that given these you can find the right answer quickly. for example the units digit of the answer can be quickly calculated (it is 3), so if you had 5 answer choices and only one of those had 3 in its unit digit - you could have your answer very quickly.
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28 Apr 2007, 06:30
1! = 1 (units digit 1)
2! = 2 (ud 2)
3! = 6 (ud 6)
4! = 24 (ud 4)
5!, 6!.... the units digit will be 0 because all the terms will include 5x2=10

units digit of 1!+2!+... will be 1+2+6+4+0+0+0.... = 3

No shortcut to make the calculation then?
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28 Apr 2007, 06:32
from 5! (i.e. 5!, 6!, 7! ...) the units digits is 0
so the units digit of the sum 1!+...+20! depends only on the units digits of 1!+2!+3!+4! = 1+2+6+24 = 33
hence the units digits of the complete sum is 3
similarly you can relatively easily compute the tens digit of the sum (you need to check only 1!...9!) and it will be inevitably and odd digit (or more specifically 1 if i'm not wrong with my quick no-paper calculations)

this would probably suffice to choose the right answer from a reasonable set of choices...
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Re: PS - sum of factorials [#permalink]

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28 Apr 2007, 06:37
querio wrote:
What is 1!+2!+...+20! ?

Do you guys know any trick to make such a calculation?

Thanks!

although no shortcut .... it seems that this sum may be part of a "bigger picture" question - maybe related to counting/combinatorics....
if so, it might be that the wider context situation has a shortcut that bypasses the sum of factorial altogether.
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28 Apr 2007, 07:15
Hobbit, and querio..nice work on getting the unit digit..totally bummed on this one..

weird usually my mind works better in the morning..but somehow today totally stumbled ...
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Re: PS - sum of factorials [#permalink]

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28 Apr 2007, 07:30
[quote="hobbit"][quote="querio"]What is 1!+2!+...+20! ?

Do you guys know any trick to make such a calculation?

Thanks![/quote]

although no shortcut .... it seems that this sum may be part of a "bigger picture" question - maybe related to counting/combinatorics....
if so, it might be that the wider context situation has a shortcut that bypasses the sum of factorial altogether.[/quote]

Yeah, you're right... I don't think Gmat will ask to make the calculation just to get the final number, but it will somehow hide the answer among the answer choices. Thanks!
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Re: PS - sum of factorials [#permalink]

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30 May 2014, 12:04
How about remainder of a sum of first n factorials when divided by 47?

(1!+2!+3!......45!)/47
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Re: PS - sum of factorials [#permalink]

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09 Jun 2014, 16:44
GMAT will not ask questions such as the sum of factorials to 20. Although, it is possible that they may ask the units digit of 1!+2!+3! .......+ 20! as described @querio. Instead, the types of questions that I have seen on the official GMAT follow the pattern of the examples listed below:

1) How many terminating zeroes does 100! have when written as an integer? (Answer is 24)

2) What is the largest prime factor of 13! - 11! ? (Answer is 31)

Cheers,
Dabral
Re: PS - sum of factorials   [#permalink] 09 Jun 2014, 16:44
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# PS - sum of factorials

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