Easy math puzzles
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43 members have voted
May 2nd, 2020 at 4:18:00 PM
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Good problem. I had seen it before, so stayed out of it. I wouldn't have filed it as an "easy math problem" (the title of the thread).
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
May 2nd, 2020 at 4:54:32 PM
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Quote: WizardGood problem. I had seen it before, so stayed out of it. I wouldn't have filed it as an "easy math problem" (the title of the thread).
Well, here's an easy one:
For what positive value p does 1 + 2 p + 3 p2 + 4 p3 + 5 p4 + ... = 25?
Show your work - none of this "I approximated it on Excel" stuff.
May 2nd, 2020 at 5:19:20 PM
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Quote: ThatDonGuyWell, here's an easy one:
For what positive value p does 1 + 2 p + 3 p2 + 4 p3 + 5 p4 + ... = 25?
Show your work - none of this "I approximated it on Excel" stuff.
Let equation A be 25=1 +2p +3p^2 etc... (the equation as stated)
Let equation B be 25p = p + 2p^2 + 3p^3 etc.
Let C equal A minus B to get 25(1-p) = 1 + p + p^2 + p^3 + p^4 etc
Let D be p*C = p + p^2 + p^3 etc
Then C minus D is 25(1-p)^2 = 1
solve to get p=4/5
Last edited by: rsactuary on May 2, 2020
May 2nd, 2020 at 5:53:43 PM
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Quote: rsactuaryLet equation A be 25=1 +2p +3p^2 etc... (the equation as stated)
Let equation B be 25p = p + 2p^2 + 3p^3 etc.
Let C equal A minus B to get 25(1-p) = 1 + p + p^2 + p^3 + p^4 etc
Let D be p*C = p + p^2 + p^3 etc
Then C minus D = 25(1-p)^2 = 1
solve to get p=4/5
Correct.
Another way to do this is to note that:
1 + 2 p + 3 p2 + 4 p3 + ... = (1 + p + p2 + p3 + ...)2.
May 2nd, 2020 at 6:00:05 PM
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Quote: ThatDonGuyCorrect.
Another way to do this is to note that:
1 + 2 p + 3 p2 + 4 p3 + ... = (1 + p + p2 + p3 + ...)2.
Yeah, it's been too long since I did stuff like this on a regular basis or I would have recognized that. I kind of got there by first principles.
May 2nd, 2020 at 7:11:00 PM
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This one made a splash in India a few years back.
Have you tried 22 tonight? I said 22.
May 3rd, 2020 at 5:20:49 AM
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Quote: GialmereThis one made a splash in India a few years back.
I count
18
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
May 3rd, 2020 at 11:30:10 AM
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Quote: unJonI count
18
Correct!
Your geometry teacher would be proud.
Have you tried 22 tonight? I said 22.
May 3rd, 2020 at 12:24:52 PM
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You're playing a track and field board game with your family during the lockdown. If each of the runner pawns travels the indicated number of spaces every turn, at which numbered spot will all of the runners end up next to one another?
Have you tried 22 tonight? I said 22.
