add 2sqrt(5) - 3sqrt(2) + 4sqrt(5)
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No. But it’s really close.
The left hand side may be written as
X=∏∞k=2k1/2k−1
Take its logarithm
lnX=∑∞k=2lnk2k−1
Performing the sum using Sum[Log[n]/2^(n-1),{n,2,Infinity}] - Wolfram|Alpha Results
lnX≈1.01567
If the equation was correct, then lnX would have been equal to 1.
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