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Re: Algebra: PS Diagnostic Test
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07 Oct 2022, 10:14
18. The infinite sequence \(a_1, \ a_2, \ …, \ a_n, \ …\) is such that \(a_n = n!\) for \(n > 0\). What is the sum of the first 11 terms of the sequence?
A. 43954414
B. 43954588
C. 43954675
D. 43954713
E. 43954780
\(a_1 = 1!, a_2 = 2!, a_3 = 3!, a_4 = 4!, a_5 = 5!, a_6 = 6!, a_7 = 7!, a_8 = 8!, a_9 = 9!, a_10 = 10!, a_11 = 11!\)
Sum\( = 1! + 2! + 3! + 4! + 5! + 6! + 7! + 8! + 9! + 10! + 11!\)
Best way to approach this would be to analyze the answer choices and use POE:
If you notice, every answer choice has a different units digit, so let us work around that
Now, we know that every term of the above sum from 5! onwards to 11! ends with 0 in the units digit place
So, we basically need to calculate the Units digit of \(1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33\), so Units digit = 3
Only one answer choice has a Units digit = 3
Answer: D