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]

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?

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?

I did the same too. Can someone enlighten us on this?

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