1+x+x^2+x^3+....
You asked:
Find the sum of the sequence: \(1\), \(x\), \({x}^{2}\), \({x}^{3}\),\(\ldots\)
MathBot Answer:
The infinite series \(\displaystyle \sum_{n=1}^{\infty} x^{n - 1}\) diverges.
This is a geometric sequence.
The nth term in this sequence is given by the formula:
Explicit Formula: $$a_n=x^{n - 1}$$
Recursive Formula: $$a_n=x a_{n-1}, \text{where } a_1=1$$