ickplant@lemmy.world to Lemmy Shitpost@lemmy.world · 1 year agoPaniki.postimg.ccimagemessage-square145fedilinkarrow-up11.32Karrow-down151
arrow-up11.26Karrow-down1imagePaniki.postimg.ccickplant@lemmy.world to Lemmy Shitpost@lemmy.world · 1 year agomessage-square145fedilink
minus-squareSnazz@lemmy.worldlinkfedilinkarrow-up1·edit-21 year agoYou can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series. Sum(ar^n, n=0, inf) = a/(1-r) So, …999999 = 9 + 90 + 900 + 9000… = 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3… = Sum(9x10^n, n=0, inf) = 9/(1-10) = -1
minus-squareSnazz@lemmy.worldlinkfedilinkarrow-up1·edit-21 year agoBecause you could argue that the series converges to …999999 in some sense
You can also prove it a different way if you allow the use of the formula for finding the limit of the sum of a geometric series on a non-convergent series.
Sum(ar^n, n=0, inf) = a/(1-r)
So,
…999999
= 9 + 90 + 900 + 9000…
= 9x10^0 + 9x10^1 + 9x10^2 + 9x10^3…
= Sum(9x10^n, n=0, inf)
= 9/(1-10)
= -1
But why would you allow it?
Because you could argue that the series converges to …999999 in some sense