Find the sum of the series.
-$$x ^ { 6 } + x ^ { 7 } + x ^ { 8 } + x ^ { 9 } + \ldots$$
A) $\frac { x ^ { 5 } } { 1 - x }$
B) $\frac { x ^ { 6 } } { 1 + x }$
C) $\frac { x ^ { 6 } } { 1 - x }$
D) $\frac { 6 x } { 1 - x }$

Question

Quizplus · Accepted Answer

We can write the series as 
$$x^6(1+x+x^2+x^3+\ldots)$$
Using the formula for an infinite geometric series, we have 
$$\sum_{n=0}^{\infty} x^n = \frac{1}{1-x}$$
Thus, the sum of the series is 
$$x^6\cdot \frac{1}{1-x} = \boxed{\frac{x^6}{1-x}}.$$

Find the Sum of the Series x6+x7+x8+x9+…x ^ { 6 } + x ^ { 7 } + x ^ { 8 } + x ^ { 9 } + \ldotsx6+x7+x8+x9+…

Find the Sum of the Series $x ^ { 6 } + x ^ { 7 } + x ^ { 8 } + x ^ { 9 } + \ldots$