Above shows real numbers that belong to an arithmetic progression in order. Find the next term of this sequence.
Find the number of -term strictly increasing geometric progressions, such that all terms are positive integers less than
If satisfies the equation above and it can be represented as for positive integers , , , and , where is prime, determine the smallest value of .
The image above shows a broken line (a series of connected line segments) starting at the origin, O. The nth segment in the broken line has length , and at the end of each segment, the broken line turns counter-clockwise.
As the number of segments in the broken line approaches infinity, the final endpoint of the broken line approaches a point P. The distance OP can be written as , where a and b are positive coprime integers. Find .
Evaluate the sum above in degrees.