- #1
maxkor
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Calculate $2\sqrt{2\sqrt[5]{2\sqrt[8]{2\sqrt[11]{2 \cdots}}}}$.
I know only that $...=2^{1+{1\over2}+{1\over10}+{1\over80}+{1\over880}+\ldots}$
I know only that $...=2^{1+{1\over2}+{1\over10}+{1\over80}+{1\over880}+\ldots}$
The value of $2\sqrt{2}$ when calculated to infinity is an irrational number, meaning it has an infinite number of decimal places and cannot be expressed as a fraction. It is approximately equal to 2.82842712475.
To calculate $2\sqrt{2}$ to infinity, you can use the formula for finding the limit of a sequence. This involves taking the square root of 2, multiplying it by 2, and then repeating the process infinitely. This will result in an increasingly accurate approximation of the value of $2\sqrt{2}$ to infinity.
$2\sqrt{2}$ to infinity is an irrational number. This means it cannot be expressed as a ratio of two integers and has an infinite number of decimal places.
Calculating $2\sqrt{2}$ to infinity is significant in mathematics as it helps us understand the concept of infinity and irrational numbers. It also has applications in fields such as geometry, physics, and engineering.
No, $2\sqrt{2}$ cannot be calculated to a precise value as it is an irrational number. However, we can approximate its value to any desired level of accuracy by using advanced mathematical techniques such as calculus.