promotion image of download ymail app
Promoted

GMAT math question - please help!?

For every integer k from 1 to 10 inclusive, the kth term of a certain sequence is given by (-1)^(k+1) * (1/2^k). If T is the sum of the first 10 terms in the sequence, then T is:

A) greater than 2

B) between 1 and 2

C) between 1/2 and 1

D) between 1/4 and 1/2

E) less than 1/4

Is there a way to answer this without having to sub in all 10 values for k? I have less than 120 seconds to answer questions like this on the GMAT exam...

Thank you!

6 Answers

Relevance
  • 1 decade ago
    Favorite Answer

    alternating series are bounded by their partial sums

    In English that means if you have a sum like this: 1/2 - 1/4 + 1/8 -1/16 + 1/32 - 1/64 then the final answer is between any two "cut offs" so the final answer is between 1/2 and 1/2-1/4=1/4, the final answer is also between 1/2-1/4=1/4 and 1/2-1/4+1/8=3/8. The actual final answer to a+ar+ar^2+... (called a geomteric series) is a/(1-r) so in your problem the answer (when yous um to infinity) is (1/2)/(1-(-1/2))= (1/2)/(3/2) = 1/3. So the sum of the first 10 will be close to this final answer of 1/3

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    Sure.

    The series is

    1/2 - 1/4 + 1/8 - ...

    Note that the series is alternating and the absolute value of each term is less than that of the preceeding term. So the final value is between the first term and the sum of the first two terms. That is to say, the sum is between 1/2 and (1/2 - 1/4 = 1/4). As each additional term is added, the sum stays within those bounds.

    So the answer is d.

    • Commenter avatarLogin to reply the answers
  • binnu
    Lv 4
    4 years ago

    on the grounds that 9 is unusual 9* is 9 cases 3=27 on the grounds that 6* is even 6* is 6 cases a million/2=3 9* x 6* would desire to be 27X3=80 one Does the respond e book say 27* or 27? If it says 27*, 27* could be 27X3 as a results of fact it somewhat is unusual and could be comparable to an answer of 80 one. are additionally you specific the question did not ask for 9X6* which may well be 9x3=27? If neither of those are the case than i could agree including your answer. Is there any way you may submit a link to the positioning with the question on right here?

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    e

    sub 1 and you get 1/4

    sub 10 and you get a very samll negative fraction

    thus every odd will give you a 1 * a smaller fraction then 1/4

    every even will give you a negative so then the sum must be less then 1/4

    there are always tricks to these problems to do them fast

    • Commenter avatarLogin to reply the answers
  • How do you think about the answers? You can sign in to vote the answer.
  • 1 decade ago

    This is - sum (1 to 10) (-1/2)^k

    There is a formula for the geometric proggression

    I think it's this one: sum (1 to n) (a)^k = [1-a^(n+1)]/(1-a)

    Ana

    • Commenter avatarLogin to reply the answers
  • 1 decade ago

    the sum is

    T = 1/2 - 1/4 + 1/8 - 1/16 ......... 1/(2^9) - 1/(2^10)

    = 1/4 + 1/16 ...... 1/(2^10)

    thus 1/4 < T < 1/2

    • Commenter avatarLogin to reply the answers
Still have questions? Get your answers by asking now.