Use geometric series to show that the total submission { theta, n =0} X^n = 1/1-

Question

Use geometric series to show that the total submission { theta, n =0} X^n = 1/1-x for |x| < 1

Which of the following equations represents the sum of an infinite geometric series?

S = a1/ 1-r^2

(B) S = 2a1/1-r

(C) S = a1/1-r

(D) S = a1/ 1-r

Compare the equation for the sum of an infinite geometric series to the given infinite sum.

What are a1 and r1

(A) a1 = 1 and r = x^n

(B) a1 = 1 and r= x

(C) a1 =1-x  and  r= 1

(D) a1 =0 and r =x

Substituting the values for a1 and r into the equation for the sum of an infinite geometric series obtains which final equation?

(A)  S = 1/1-x

(B) S = 1/1+x

(C) S = 1/1-x^n

(D) S = 1/1+x^n

Explanation / Answer

(C) S = a1/1-r

(B) a1 = 1 and r= x

(A) S = 1/1-x

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