Unexpexted Answers
Level
pending
1-1+1-1+1-1+1-1+1-1 .......................=¿¿??
1/2
1
0
1/2 , 1 , 0
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
This is known as Grandi's series. There is an interesting numberphile video on it!
(1 − 1) + (1 − 1) + (1 − 1) + … = 0 + 0 + 0 + … = 0.
1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + … = 1 + 0 + 0 + 0 + … = 1.
S = 1 − 1 + 1 − 1 + …, so 1 − S = 1 − (1 − 1 + 1 − 1 + …) = 1 − 1 + 1 − 1 + … = S = 1/2