Question of the week 21-Jan-2018

The value of  2 - 2² + 2³ - 2⁴ + 2⁵ - ...…. (infinite terms) is

a) -2              b) 2/3              c) -2/3                d) None of these

Answer to the previous week question here. Next week question here. I expect that most would answer it incorrect and it is very much a CGL level question. Keep in mind that i promised you i wouldn't ask basic or stupid questions. So, Pls think twice before you answer. This question is part of my upcoming book and it is solvable in less than 10 seconds. Your answer only with a logical explanation is welcomed in the comments section. Stay tuned for the technique and the answer. I am  making sure that my upcoming book is with many such beautiful problems. Reading it will provoke new thoughts and bring out the best in you.

Solution (31-Jan-18):

If you have used the formula S = a/1-r, then you are trapped. In fact such answer is readily available to trap you. Pls keep in mind that the above formula can be used only if -1 < r < 1. In the given sum, the value of 'r' is 2 and hence it can't be applied.

In fact, such series can't be evaluated to any finite value. So, the answer should be 'd'.

Proof is not needed. Wanted to know the proof about -1 < r < 1 ? See here.