Add it up

rrusczyk

How far do I have to go in the sum

1 + 1/2 + 1/3 + 1/4 + 1/5 + . . .

until I have a total that is greater than $2\frac{1}{2}$ ?

(I mean, what is the last term I have to include in that sum to get a sum that is greater than $2\frac{1}{2}$ )

**Posted:** Wed Jan 12, 2005 11:43 am

shinwoo · Yang-Mills Theory Offline Joined: 30 Oct 2004 Posts: 702

This is a pretty interesting question..

what I woud do is change 2 and 1/2 to a mixed fraction which is 5/2

5/2 - 1 = 3/2
3/2 - 1/2 = 2/2
3/3 - 1/3 = 2/3
8/12 - 4/12 = 4/12
4/12 - 3/12 = 1/12
5/60 - 12/60 = wich becomes negative

so it's 12/60 = 1/5

**Posted:** Wed Jan 12, 2005 12:26 pm

JBL

Shinwoo, you made a tiny mistake there -- why don't you try it again? (Your method is good!)

**Posted:** Sat Jan 15, 2005 3:22 pm

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shinwoo · Yang-Mills Theory Offline Joined: 30 Oct 2004 Posts: 702

Ah!!!

I will fix it after the foot ball game Mr. Green

Go STEELERS!!

**Posted:** Sat Jan 15, 2005 3:43 pm

Mamat · Poincare Conjecture Offline Joined: 26 Sep 2004 Posts: 189

I think the last term is 1/7

**Posted:** Sat Feb 05, 2005 2:29 pm

shinwoo · Yang-Mills Theory Offline Joined: 30 Oct 2004 Posts: 702

you know,i sadi I would fix my mistake after the football game, but I never fixed it Blush

so, what did I do wrong? Sad

**Posted:** Sun Feb 06, 2005 9:59 am

JBL

Look at the values you subtracted -- first you took out 1, then 1/2, then 1/3, then what?

**Posted:** Sun Feb 06, 2005 10:24 am

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LONGMAN · New Member Offline Joined: 21 Feb 2005 Posts: 2

With calculator?
ha.......

**Posted:** Mon Feb 21, 2005 7:27 am

math92

i think JBL is right, i don't see where 4/12 came in

**Posted:** Mon Apr 18, 2005 1:29 pm

GoBraves

Why are so many old topics coming back???

**Posted:** Mon Apr 18, 2005 3:39 pm

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**Posted:** Mon Apr 18, 2005 5:19 pm

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**Posted:** Mon Apr 18, 2005 8:43 pm

Raenef

start with what shinwoo did
5/2 - 1 = 3/2
3/2 - 1/2 = 2/2
2/2 - 1/3 = 2/3
2/3 - 1/4 = 8/12 - 3/12 = 4/12
4/12 - 1/5 = 20/60 - 12/60 = 8/60
8/60 - 1/6 = 8/60 - 10/60 = -2/60
which is negative, so its actually 1/6
just a tiny mistake

**Posted:** Tue Apr 19, 2005 11:17 am