If N is an integer, what is the units digit of (N-1)! + N! + : DS Archive
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# If N is an integer, what is the units digit of (N-1)! + N! +

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Intern
Joined: 03 Aug 2009
Posts: 6
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Kudos [?]: 3 [0], given: 1

If N is an integer, what is the units digit of (N-1)! + N! + [#permalink]

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23 Aug 2009, 15:04
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If N is an integer, what is the units’
digit of (N-1)! + N! + (N + 1)! + 2^N(3^N+1)?

(1) N > 2
(2) N = 3K + 1, where K is an integer
greater than 1.
Senior Manager
Joined: 23 Jun 2009
Posts: 361
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 5

Kudos [?]: 130 [1] , given: 80

Re: (N-1)! + N! + (N + 1)! + 2^N(3^N+1) [#permalink]

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24 Aug 2009, 05:48
1
KUDOS
Say that as f(n) = $$(N-1)! + N! + (N + 1)!$$ + $$2^N$$.$$(3^N+1)$$
f(1)=0
f(2)=9
f(3)=6
f(4)=2
f(5)=2
for every n>5; f(n)=
if n mod 4 = 0 than 2
if n mod 4 = 1 than 8
if n mod 4 = 2 than 0
if n mod 4 = 3 than 4

A insuff, N>2 does not mean anything
B insuff N=3K+1 does not mean anything (K = 0, N=1, f(n)=0, K=1, N=4, f(n)=2, K=2, N=7, f(n)=4 etc.)
together insuff
we do not know what K is, so f(n) can be any of the results written above.
Re: (N-1)! + N! + (N + 1)! + 2^N(3^N+1)   [#permalink] 24 Aug 2009, 05:48
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