Question

Find the sum (assume |x|<(1/2)):
1+2x+4x^2+8x^3+16x^4+...=?

Answer 1

x is in the following interval:\[\left| x \right|< \frac{ 1 }{ 2 } \implies -\frac{ 1 }{ 2 } < x < \frac{ 1 }{ 2 }\]So x can really be any value in that interval. How could be compute a sum when the variable itself could take on many values? Therefore, we can't compute the sum here.

@iderek