The product 2(1/4)⋅ 4(1/16) ⋅ 8(1/48) ⋅ 16(1/128)⋅ ldots to ∞ is equal to :

Question

The product 2(1/4)⋅ 4(1/16) ⋅ 8(1/48) ⋅ 16(1/128)⋅ ldots to ∞ is equal to : (A) 2(1/4) (B) 2 (C) 2(1/2) (D) 1

Tardigrade Admin · Accepted Answer

2(1/4)⋅ 4(1/16) ⋅ 8(1/48) ⋅ 16(1/128)⋅ ldots ∞ =2(1/4)⋅ 4(2/16) ⋅ 8(3/48) ⋅ 16(4/128)⋅ ldots ∞ -2(1/4)⋅ 4(1/8) ⋅ 8(1/16) ⋅ 16(1/32)⋅ ldots ∞ =2(1/4)+(1/8)+(1/16)+(1/32)+.......∞=(2)((1/4/1-1/2))=21/2

Q. The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 1 6^{\frac{1}{128}} \cdot \dots$ to $\infty$ is equal to :

$2^{\frac{1}{4}}$

$2$

$2^{\frac{1}{2}}$

$1$

Q. The product 241​⋅4161​⋅8481​⋅161281​⋅… to ∞ is equal to :

241​

2

221​

1

241​⋅4161​⋅8481​⋅161281​⋅…∞ =241​⋅4162​⋅8483​⋅161284​⋅…∞ −241​⋅481​⋅8161​⋅16321​⋅…∞ =241​+81​+161​+321​+.......∞=(2)(1−1/21/4​)=21/2

Q. The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 1 6^{\frac{1}{128}} \cdot \dots$ to $\infty$ is equal to :

$2^{\frac{1}{4}}$

$2$

$2^{\frac{1}{2}}$

$1$