explanation for tree riddle needed?

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karen

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first year of the tree growth is 1meters, what would the height of the tree be after 1000 years if each year is the half the height
example, 1+1/2+1/4+1/8....and so on
THE ANSWER IS 2, BUT wat i want to know is HOW DO YOU GET IT??(the explanation) please use words rather for symbols like ^, *, i know the basics like -,+,
explain the formulas that ur using plz. it won't do me any good just giving me the numbers

im a curious type knowing the answer and not the explantion is the worst thing u can do to me lol
 
Well the answer isn't really going to be 2, but it's getting really, really close to 2. The key here is not to look at the height of the tree, but how far away it is from being 2 meters tall.

After the first year, it's 1 meter tall, which means that it's 1 meter away from being 2 meters tall.

In the second year, it grows 1/2 meters. This makes it 1 1/2 meters tall. But another way of thinking about this is that it is now 1/2 meters away from being 2 meters tall.

In the third year, it grows 1/4 meters. Now it is only 1/4 meters away from being 2 meters tall.

In the fourth year, it grows 1/8 meters. Now it is 1/8 meters away from being 2 meters tall.

Now we look at the general pattern. Each year, the difference between the tree's height and 2 meters is divided in half:

Year 1: 1
Year 2: 1/2
Year 3: 1/4 = 1/(2x2)
Year 4: 1/8 = 1/(2x2x2)
Year 5: 1/16 = 1/(2x2x2x2)

After 1,000 years, the difference between the tree's height and 2 meters will be 1 over 2^999, which means 2 multiplied with itself 999 times. This number is really, really small. If you wanted to write it out as a decimal, it would be approximately

0.00000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
000000000000000000000000000
00002

This fraction of a meter is much, much smaller than a single atom. So for all practical purposes, the height of the tree after a thousand years might as well be 2 meters.
 
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