for every integer k..perplexing?

[coolgirl26]

how to solve..i got it wrong!!!

[DanaJ]

The problem is about a geometrical progression. Because the explanation would have been hard to write without an equation editor, please see picture.

[Feep]

The above answer is absolutely correct, but geometric sums can be tricky, especially if you don't know the proper formulae. Attempting to derive the about result in two minutes would be fairly difficult.

Since the solutions do not require a specific answer, estimation is your best friend here. The sequence is 1/2 - 1/4 + 1/8 - 1/16 + 1/32... Each term becomes exponentially less relevant to the total.

After computing the sum of the first three terms (3/8), it should be clear that no single term after it is going to bring this sum below 2/8 or above 4/8, for obvious reasons. So you can pretty safely choose the correct answer.