The value of 61 - 2- 61 - 4- 61 - 8- is

We have, 6^1/2×6^1/4×6^1/8×⋯∞ =6^[1/2+1/4+1/8+⋯+∞] nbsp; =6^(1/2)/(1 1/2)=6^1=6 ...

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Sum of Infinite Terms of a GP

The value of ...

Question

The value of $6^{1 / 2} \times 6^{1 / 4} \times 6^{1 / 8} \times \dots \infty$ is

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Solution

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6^{\frac{1}{2}} \times 6^{\frac{1}{4}} \times 6^{\frac{1}{8}} \times 6^{\frac{1}{16}} \times . .

6^{\frac{1}{2}} \times 6^{\frac{1}{2}} \times 6^{\frac{3}{8}} \times 6^{\frac{1}{4}} \times . . . . . . . . .

6^{1 / 2} \times 6^{1 / 4} \times 6^{1 / 8}

\infty = 6

6^{\frac{1}{2}} \times 6^{\frac{1}{4}} \times 6^{\frac{1}{8}} . . . . . \infty = 6

- 61 + . . . . . . . = \frac{2}{3} + (- 61)

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