11. With his method, he was able to reduce this evaluation to the sum of geometric series . 12. In mathematics, the infinite series is an elementary example of a geometric series that converges absolutely. 13. Both of these sums can be derived by using the formula for the sum of a geometric series . 14. They vary and often deviate significantly from any geometric series in order to accommodate traditional sizes when feasible. 15. The first equality is given by the formula for a geometric series in each term of the product. 16. In modern mathematics, that formula is a special case of the sum formula for a geometric series . 17. Converges for all | z | ( for instance, by the comparison test with the geometric series ). 18. Moreover, one of Ahmes'methods of solution for the sum suggests an understanding of finite geometric series . 19. A similar phenomenon occurs with the divergent geometric series proofs demand careful thinking about the interpretation of endless sums. 20. The geometric series and continued fraction articles are a bit complicated, yes, but certainly not needed here.
