Question

Use the geometric series formulas to find the sum of the geometric series.

Answer 1

Answer:

The sum of the geometric progression is $S_n=(x^{31}+1)/(x+1)$.

Step-by-step explanation:

Given data in the question:-      

$1-x+x^2-x^3+x^4+........+x^{30}$

We have to find the sum of Geometric Progression.

Solution:-      

As we know the sum of geometric progression is

$S_n=a(r^n-1)/r-1$

Where r is the common ratio defined as $r=T_n/T_{n-1}$

$r=-x/1$

n(no of terms)=31

$S_n=1((-x)^{31}-1)/(-x-1)\\S_n=-(x^{31}+1)/-(x+1)\\S_n=(x^{31}+1)/(x+1)$