SOLUTION: A kangaroo hops in such a way that the distance covered in each hop is half that of the previous one. The kangaroo started bouncing from a tree and hopped a distance of 2 m. on

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Question 772715: A kangaroo hops in such a way that the distance covered
in each hop is half that of the previous one. The
kangaroo started bouncing from a tree and hopped a
distance of 2 m. on his third hop. How far is the kangaroo
from the tree after its tenth hop?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the kangaroo hops +a+ m on the
1st hop, each succeeding hop is:
+a%2A2%5E%28-n%29+, where +n+ = 0,1,2,3. . . .
The sum = +a%2A%28+2%5E0+%2B+2%5E%28-1%29+%2B+2%5E%28-2%29%29+ . . .
The formula for the geometric sum is:
+a%2A%28+1+-+r%5En%29+%2F+%28+1+-+r+%29+
In this case, +a+=+2+, +r+=+1%2F2+, +n+=+10+
Sum = +2%2A%28+1+-+%28+1%2F2%29%5E10+%29+%2F+%28+1+-+1%2F2+%29++
Sum = +2%2A%28+1+-+1%2F1024+%29+%2F+%281%2F2%29+
Sum = +4%2A%28+1023%2F1024+%29+
Sum = +1023%2F256+
Sum = +3.9961+
The kangaroo is 3.9961 m from the tree