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15 Oct 2006, 16:29
Kudos
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(-1)^k+1(1/2^k) If this equation determines the terms in a sequence and k is the numbers 1-10, inclusive, and T is the sum of the first 10 terms in this sequence, what is the value of T?
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15 Oct 2006, 16:55
Kudos
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uphillclimb
well I'm sure there is much better way of doing this but here is my stab at it without benefit of having to eliminate answers:
so ever odd k is +ve fraction, every even -ve
1/2 - 1/4 + 1/8 - 1/16 + 1/32 - 1/64 + 1/128 - 1/256 + 1/512 - 1/1024, from here I can see that sum will be somewhere between 1/2 and 1/4
however math is not hard, so it will be:
1/4 + 1/16 + 1/64 + 1/256+1/1024
[256 + 64 + 16 + 4 + 1] / 1024 = 341/1024 ?
15 Oct 2006, 20:01
Kudos
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what does 1(1/2^k) means?
if it is 1*(1/2^k). then the result is 1-1/(2^10) = 1023/1024.
When u add them, (-1)^k will eliminate each other.
you are left with
1/2 + 1/2^2 + 1/2^3 + 1/2^10
= (1/2 + 1/2^2 + 1/2^3 + 1/2^10 + 1/2^10) - 1/2^10.
then add the one in the bracket from the back to the front, you can easily get it equals 1.
then u get the result.
if it is 1*(1/2^k). then the result is 1-1/(2^10) = 1023/1024.
When u add them, (-1)^k will eliminate each other.
you are left with
1/2 + 1/2^2 + 1/2^3 + 1/2^10
= (1/2 + 1/2^2 + 1/2^3 + 1/2^10 + 1/2^10) - 1/2^10.
then add the one in the bracket from the back to the front, you can easily get it equals 1.
then u get the result.
