Sum of all reals

Level pending

Assuming that 1-1+1-1+1-1…..=1/2, give a finite value to 12xS where S=1+2+3+4… (S is the sum of all natural numbers.)


The answer is -1.

Tom Kovar. by tom kovar. , 26, USA

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

Tom Kovar.
Jan 11, 2015

X=1-2+3-4…., 2X=1+(-2+3-4…) +(1-2+3…), 2X=1-1+1-1…, X=1/4, S-X=(1+2+3+4…) -(1-2+3-4…), S-X=4+8+12…., S-X=4S, -3S=X, -3S=1/4, S=-1/12, 12s=-1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

There's a mistake right at the begining. If X = 1-2+3-4..., then 2X = 1-(2-3+4...)+(1-2+3...). Anyway you got right to 2x=1-1+1-1. And S=-1/12 is well know :)

Roberto Villadangos Carrera - 6 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...