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# Does PS include questions on sequences and series? Also,

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Intern
Joined: 04 Dec 2003
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Does PS include questions on sequences and series? Also, [#permalink]  05 Dec 2003, 08:32
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Does PS include questions on sequences and series?

Also, can someone help me with this one -
Q -What is the sum of reciprocal of first thirty positive integers?

Thx
Director
Joined: 28 Oct 2003
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Location: 55405
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What is the sum of reciprocal of first thirty positive integers?

I don't know a shortcut to get the right answer, but if the question is multiple choice: I'd look at the answers, and if they're spaced widely enough, compute the sum of the first ten reciprocals + 10(1/15) +10(1/25).

I'm curious as to whether someone will have a more elegant and fast solution.
Intern
Joined: 04 Dec 2003
Posts: 4
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Thanks!
This might sound silly but how did you get 10(1/50) and 10(1/25)?
Director
Joined: 28 Oct 2003
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10(1/15) is an approximation of the sum of 1/11+1/12+1/13...+1/20
10(1/25) is an approximation of the sum of 1/21+1/22+1/23...+1/30

I just picked the midpoint.

Converting 1-10 to decimals (3 places) is easy if you have them memorized.
1+.5+.333+.25+.2+.167+.143+.125+.111+.1 =

2.92

+10/15 +10/25
+.667+.400

3.987, approximately...
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

Per Microsoft Excel, the exact solution is
9304682830147/2329089562800

Or, in decimal form, 3.994987130920390

I learned that Excel has an LCM function.

Considering how much of my employer's time I just wasted, I am ashamed of myself.
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