k=1: first term = 1/2
k=2: second term = -1/4
...
k=10: tenth term = -1/2^10
T=summation of first 10 terms
= (1/2 - 1/4) + (1/8 - 1/16) + ... + (1/512 - 1/1024)
this is Geometric Progression
S(n) = a*(1-r^n) / (1-r)
here a=1/2; r=(-1/4) / (1/2) = -1/2; n=10
=> S(10) = (1/2) * (1-(-1/2)^10) / (1-(-1/2))
=> S(10) = (1/2) * (1-(1/2)) / (3/2)
= (1/2) * (1/2) / (3/2)
= 1/6 < 1/4
Hence [E]
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GMAT PREP sequence question help
Source: Beat The GMAT — Problem Solving |
Is there a way to solve this w/out knowing that it's a geometric progression? I was adding it all by hand and it was taking forever. any shortcuts besides geometric progression?
I did the same too. Can someone enlighten us on this?semidevil wrote:Is there a way to solve this w/out knowing that it's a geometric progression? I was adding it all by hand and it was taking forever. any shortcuts besides geometric progression?
kanha81,
Thanks for the solution.
Stating that it was geometric progression was really helpful because all i had to do was to do a little research on geometric progression and found out what it was and as a result i got to know about arithmetric progression as well.
Thanks
Thanks for the solution.
Stating that it was geometric progression was really helpful because all i had to do was to do a little research on geometric progression and found out what it was and as a result i got to know about arithmetric progression as well.
Thanks
we don't need G.P for this. once we simplify the function for different values ranging from 1 to 10 inclusive, we find a series as below:
(1/2 -1/4) + (1/8 - 1/16) + .....
Observe that the first group inside the bracket yields 1/4
the second group will yield 1/16
this will continue.
so, obviously the answer is more than 1/4. but it will never be 1/2, as we each successive group becomes even smaller than the previous one. So, ans will be (D).
hope this helps.
(1/2 -1/4) + (1/8 - 1/16) + .....
Observe that the first group inside the bracket yields 1/4
the second group will yield 1/16
this will continue.
so, obviously the answer is more than 1/4. but it will never be 1/2, as we each successive group becomes even smaller than the previous one. So, ans will be (D).
hope this helps.
