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Sum of a series (Further Math)

S = 1!+2!+3!.....+infinity!
Find the last digit of S.
Reply 1
Avatar for mqb2766
mqb2766
21
Original post by RohanHowl
S = 1!+2!+3!.....+infinity!
Find the last digit of S.

Ignoring the fact it doesn't exist, what are the values of the first 6 terms say, how does that get you the answer?
Reply 2
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RohanHowl
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Original post by mqb2766
Ignoring the fact it doesn't exist, what are the values of the first 6 terms say, how does that get you the answer?

1,2,6,24,120,720 are the first six terms but I didn't get your question, could you clarify?
Original post by RohanHowl
1,2,6,24,120,720 are the first six terms but I didn't get your question, could you clarify?

What simple useful fact do you know about all of the subsequent terms?
Reply 4
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RohanHowl
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Original post by Plücker
What simple useful fact do you know about all of the subsequent terms?

The nth term is the product of the index(n) and the previous term. Like 2*1=2, 3*2=6, 4*6=24.
Original post by RohanHowl
The nth term is the product of the index(n) and the previous term. Like 2*1=2, 3*2=6, 4*6=24.

This question is all about the last digit.
Reply 6
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RohanHowl
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Original post by Plücker
This question is all about the last digit.

Ah I get it now. So the answer is 3 if I'm not wrong?
Original post by RohanHowl
Ah I get it now. So the answer is 3 if I'm not wrong?

That is correct.
Reply 8
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RohanHowl
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Original post by Plücker
That is correct.

Thanks for the help.
i get it now thankss! @Plucker
for anyone still stuck n! is a multiple of 10 for all n >= 5 (cos there's got to be *everything else* multiplied by 2 multiplied by a 5 in there)

so you just need to add up the low ones and find the last digit

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