tricky sum
S= 1-1+1-1+1-1+1-1... What is the value of S when it tends to infinity?
The answer is 0.5.
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1 solution
This question has 3 answers, 1, 0, and 0.5.
If you put the question as 1 + ( − 1 + 1 ) + ( − 1 + 1 ) + . . . you get an answer of 1.
If you put the question as ( 1 − 1 ) + ( 1 − 1 ) + . . . you get answer of 0.
Finally, if you put the question like this:
S = 1 − 1 + 1 − 1 + . . .
1 − S = 1 − ( 1 − 1 + 1 − 1 + . . .
1 − S = − 1 + 1 − 1 + 1 − . . .
1 − S = S
S = 0 . 5 .
This is not a good problem as it has 3 answers.
I think this sum is does not exist
This problem shows one of the greatest series that has troubled mathematicians for many years; it is known as the Grandi's series.
This series can be solved using three methods and each one provides a different answer.
This article may provide more information on this series. I just entered each one of those 3 answers and finally solved the problem.