perplexus.info :: Just Math : Find the real number

Find the real number (Posted on 2024-04-25)

Determine the possible real value of n such that:

Arctan(1/3)+Arctan(1/4)+Arctan(1/5)+Arctan(1/n)= Arctan(1)

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Computer solution (spoiler)

| Comment 1 of 5

It doesn't seem like there is a closed form analytical solution (assuming we are using radians, not degrees).

Wolfram Alpha gives the irrational number of

47.00709134262667 (continues)

as the only solution.

This is not correct - see the solutions posted by others.

Edited on April 26, 2024, 6:01 pm

Posted by Kenny M on 2024-04-26 04:59:59

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