Q Prove that 312× 314×318 = 3 Q Let x = 1+ a+a2 + - Maths - Sequences and Series

Question

Q Prove that 3 1 2 ×   3 1 4 × 3 1 8   =
  3
Q Let x = 1+ a+a2 + and y = 1+b+b2+ , where
|a| < 1 and |b| â€‹ < 1 Prove that

1 + a b + a 2 b 2   +     =   x y x + y - 1

Shruti Tyagi · Accepted Answer

Dear Student,

Question 5

312×314×318× =3⇒312+14+18+ 12+14+18+
∞12+122+123+
∞  is an infinite GP where a=12 and r=12sum of infinite GP=a1-r⇒121-12=1212=1Hence 312+14+18+
 =31hence proved that 312+14+18+  =3

Question 6
Please refer the following links for answer to asked
queriesâ€‹

https://www meritnation
com/ask-answer/question/let-x-1-a-a2-y-1-b-b2-thn-prove-t/sequences-and-series/8548945

Regards,

Q. Prove that 3 1 2 × 3 1 4 × 3 1 8 . . . . = 3 Q. Let x = 1+ a+a2 + .... and y = 1+b+b2+..., where |a| < 1 and |b| ​ < 1. Prove that 1 + a b + a 2 b 2 + . . . . = x y x + y - 1

Q. Prove that $3^{\frac{1}{2}} \times 3^{\frac{1}{4}} \times 3^{\frac{1}{8}} . . . . = 3$
Q. Let x = 1+ a+a² + .... and y = 1+b+b²+..., where |a| $<$ 1 and |b| $<$ 1. Prove that

$1 + a b + a^{2} b^{2} + . . . . = \frac{x y}{x + y - 1}$