Conjecture no. 31

Does the sums of the reciprocals of figurate numbers equal to a transcendental number infinitely often.

Also, if a regular polygon is not being able to be constructed by a straight edge and compass then does it mean that the pattern of the reciprocals of the objects forming the non constructable polygon summed is transcendental.

https://en.m.wikipedia.org/wiki/Heptagonal_number

https://en.m.wikipedia.org/wiki/Figurate_number
Thank you,

Nunghead