Equilateral pentagon of δ can be seen from the figure: Simplifying, δ is obtained as function of α and β: The remaining angles of the pentagon can be found geometrically: The remaining angles of the orange and blue triangles are readily found by noting that two angles of an isosceles triangle are equal while all three angles sum to 180°. Then formula_7 and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle
Divergence of the sum of the reciprocals of the primes induction: The first partial sum is , which has the form . If the th partial sum (for ) has the form , then the st sum is as the st prime is odd; since this sum also has an form, this partial sum cannot be an integer (because 2 divides the denominator but not the numerator), and the induction continues. Another proof rewrites the expression for the sum of the first reciprocals of primes (or indeed the sum of the reciprocals of "any" set of primes) in terms of the least common denominator, which is the product of all