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Sums and what not?

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Sums and what not?

by coolgirl26 » Sun Apr 12, 2009 2:06 pm
how do you get the answer for this

i used the sum formula and plugged in
1st ter=1/2
last term = 1/1024

into sums formula..so it should be greater than 2..
but why am i getting it wrong
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by moutar » Sun Apr 12, 2009 2:57 pm
You are getting it wrong because there are alternating signs.

This is one way you could look at it. There are others.

T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + ...
= (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + ...
= 1/4 + 1/16 + 1/64 + ...

This sum will be a little bit more than a quarter. Thus answer D.
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by sanju09 » Mon Apr 13, 2009 2:27 am
moutar wrote:You are getting it wrong because there are alternating signs.

This is one way you could look at it. There are others.

T = 1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + ...
= (1/2 - 1/4) + (1/8 - 1/16) + (1/32 - 1/64) + ...
= 1/4 + 1/16 + 1/64 + ...

This sum will be a little bit more than a quarter. Thus answer D.
this in fact forms a geometric progression whose first tem and common ratio is each 1/4, since the common ratio is between 0 and 1, hence the sum to an infinite number of such terms would still be finite and will be equal to (1/4)/[1 - (1/4)] = 1/3. Choose the most suitable interval.
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