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- anonymous

Woodstock and snoopy were playing a game. The goal of the game was to be the first one to reach the door. Woodstock and Snoopy started the game by standing 20 feet away from the door. they each took a turn to do the following;
snoopy walked half the distance between himself and the door each turn. woodstock flew one foot the toward the door each turn.
How far was snoopy and woodstock on the FOURTH TURN?
PLEASE HELP!

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- anonymous

- schrodinger

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- anonymous

This is quite a good problem about geometric series. I will try to keep is short here.
After the first turn, woodstock is 10 foot towards the door. second turn, 5 foot, third turn, 2.5 foot, forth turn, 1.25 turn
However, snoopy after 4th turn, he's still 6 foot far away from the door.
Hope this help.

- anonymous

correction,
1.25 foot and for snoopy, (20-4)=16 foot far away from the door

- anonymous

WHY IS SNOOPY UNHAPPY AND CLAIMS THAT HE WILL NEVER REACH THE DOOR?

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- anonymous

sorry for late reply, since we have to compute the geometric series given by
\[ 20\left(\frac{1}{2}+\frac{1}{2^2}+\ldots+\frac{1}{2^n}+\ldots \right) =10 \lim_{n \to \infty} \frac{1-\frac{1}{2^{n+1}}}{1-\frac{1}{2}}=20\]
Hence, it is impossible for snoopy to attempt infinite steps to reach the door. That's why he is unhappy

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