Answer:
The sum of the geometric progression is [tex]S_n=(x^{31}+1)/(x+1)[/tex].
Step-by-step explanation:
Given data in the question:-
[tex]1-x+x^2-x^3+x^4+........+x^{30}[/tex]
We have to find the sum of Geometric Progression.
Solution:-
As we know the sum of geometric progression is
[tex]S_n=a(r^n-1)/r-1\\[/tex]
Where r is the common ratio defined as [tex]r=T_n/T_{n-1}[/tex]
[tex]r=-x/1[/tex]
n(no of terms)=31
[tex]S_n=1((-x)^{31}-1)/(-x-1)\\S_n=-(x^{31}+1)/-(x+1)\\S_n=(x^{31}+1)/(x+1)[/tex]
