For n fixed, demonstrate sum(x^k, k = 0 .. n) = 1/(1-x)+o(x^n) (little o notation)

[dantopa]

For n fixed, demonstrate:

sum(x^k, k = 0 .. n) = 1/(1-x)+o(x^n) when x->0

where o is little o notation,

 

[stapel]

For n fixed, demonstrate:

sum(x^k, k = 0 .. n) = 1/(1-x)+o(x^n) when x->0

where o is little o notation,

What did you get for the closed-form expression of the summation (apart from the limit)? What did you get when you split that result into two rational "fractions"? What were your thoughts after you reached this point?

Please be complete. Thank you!