Find the sum of the infinite series 1 + 2 + 4 + 8 +…if it exists.

32,767

65,535

131,071

none

Question

Find the sum of the infinite series 1 + 2 + 4 + 8 +…if it exists.

		
32,767
		
65,535
		
131,071
		
none

satellite73 · Answer

numbers get bigger and bigger right?

satellite73 · Answer

therefore so does the sum

geerky42 · Answer

inb4 $-\dfrac1{12}$

satellite73 · Answer

??

geerky42 · Answer

http://www.urbandictionary.com/define.php?term=inb4&defid=3632151 Since $-\dfrac1{12}$ is Ramanujan sum, and this "math astounding fact" is so common, it's annoying. Just little tease, sorry

kainui · Answer

$$S=1+2+4+8+\cdots$$$$2\times S=2+4+8+16+\cdots$$$$1+2S=1+2+4+8+\cdots$$$$1+2S=S$$$$1+S=0$$$$S=-1$$

jim_thompson5910 · Answer

@Kainui the proof falls apart when you go from `1+2S = S` to `1+S = 0`. Subtracting S from both sides has you using the form `infinity - infinity` but that's indeterminate.

geerky42 · Answer

@jim_thompson5910 I think he was just continuing the discussion of Ramanujan sum, which in that case, it's technically valid. It's just a way to assign value to divergent series.