Fraction Sum of Nested Square Roots

Find the value of the pursuit sum:

[√(10 √1) √(10 √2) … √(10 √99)]/[√(10 – √1) √(10 – √2) … √(10 – √99)]

As usual, watch the video for a solution.

Or alimony reading.

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Answer To Fraction Sum of Nested Square Roots

(Pretty much all posts are transcribed quickly without I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

Let’s separately unriddle the sums in the numerator and denominator.

Now we take the sum of both sides from 1 to n² – 1.

The transpiration from n² – k to k in the first to second line requires a little bit of explanation. If k goes from 1 to n² – 1, then n² – k takes values from n² – 1 to 1, whereas k would take the same values in reverse order from 1 to n² – 1. Thus the sums in the first and second line are equal.