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What is the value at infinity? (Not a trick question)

I have a repeating function it generates:

Up down
2 4
3 3
2 4
3 3
2 4
3 3
................ This continues infinitely

If I sum the up and down separately:
up:down
2:4
5:7
7:11
10:14
12:18
15:21
................... sums infinitely, gap is increasing 2,2,4,4,6,6,8,8...

If I then divide "up" by "down"

0.5
0.714285714
0.636363636
0.714285714
0.666666667
0.714285714
....................... this is possible infinitely

What value does "up" divided by "down" tend to after infinite passes?
Original post by Jenkins1999
I have a repeating function it generates:

Up down
2 4
3 3
2 4
3 3
2 4
3 3
................ This continues infinitely

If I sum the up and down separately:
up:down
2:4
5:7
7:11
10:14
12:18
15:21
................... sums infinitely, gap is increasing 2,2,4,4,6,6,8,8...

If I then divide "up" by "down"

0.5
0.714285714
0.636363636
0.714285714
0.666666667
0.714285714
....................... this is possible infinitely

What value does "up" divided by "down" tend to after infinite passes?

You can find a formula for the nth term. What is the nth sum-of-up? And the nth sum-of-down? And hence the nth quotient sum-of-up/sum-of-down?
5/7

Every 2 goes you're adding 5 to up and 7 to down
Original post by strungtheory
5/7

Every 2 goes you're adding 5 to up and 7 to down

Much nicer answer.
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Jenkins1999
OP
Ah... Awesome, thanks. :smile:

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