Afrog sits at one end of a table which is 2m long. in its first jump the frog goes a distance of 1m along the table, with its second jump 1/2 m, with its third jump 1/4 m and so on. after how many jumps will the frog be within 1 cm of the far end of the table?

Ah, this is an infinite sum question, or a sum of geometric sequence
when will the sum reach 1cm of the edge or about 1.99m
so

2m=200cm
within 1cm means at least 1.99m
so
we will use m and not cm for consitancy

sum of geometric sequence is

a1=first term=initial jjump=1
r=common ratio=1/2
n=?, we ar solving for that

so
we want it to equal 1.99 so




divide both sides by 2

times -1

add 1 or 2/2 to both sides

take the ln of both sides


divide both sides by ln(1/2)

use your calculatro to find that n≈7.64386
so on 7th jump, it is not yet at 1cm to the edge but at 8th jump, it is past
so 8th jump

Two because two of one thing is two.