If a, x are real numbers and |a|

Question

If a, x are real numbers and |a| <1, |x|<1, then 1+(1+a)x+(1+a+a2)x2+.... ∞ is equal to (A) (1/(1-a)(1-ax)) (B) (1/(1-a)(1-x)) (C) (1/(1-x)(1-ax)) (D) (1/(1+ax)(1-a))

Tardigrade Admin · Accepted Answer

(1/1-x)+(ax/1-x) +(a2x2/1-x)+ .... =(1/1-x)× (1+ax+a2x2+ .....)=(1/1-x). (1/1-ax)

Q. If $a, x$ are real numbers and $∣ a ∣ < 1, ∣ x ∣ < 1, t h e n 1 + (1 + a) x + (1 + a + a^{2}) x^{2} + ....\infty$ is equal to

$\frac{1}{( 1 - a ) ( 1 - a x )}$

$\frac{1}{( 1 - a ) ( 1 - x )}$

$\frac{1}{( 1 - x ) ( 1 - a x )}$

$\frac{1}{( 1 + a x ) ( 1 - a )}$

$\frac{1}{1 - x} + \frac{a x}{1 - x} + \frac{a ^{2} x ^{2}}{1 - x} + .... = \frac{1}{1 - x} \times (1 + a x + a^{2} x^{2} + .....) = \frac{1}{1 - x} . \frac{1}{1 - a x}$

Q. If a,x are real numbers and ∣a∣<1,∣x∣<1,then1+(1+a)x+(1+a+a2)x2+....∞ is equal to

(1−a)(1−ax)1​

(1−a)(1−x)1​

(1−x)(1−ax)1​

(1+ax)(1−a)1​