Numerical Series

  • A. D. R. Choudary
  • Constantin P. Niculescu


A suggestive definition (though not entirely accurate) for the notion of series, is that of a sum with infinitely many terms.


Complex Number Convergent Series Positive Term Convergence Test Nonnegative Number 
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  1. 1.
    Niculescu, C.P., Prăjitură, G.: Some open problems concerning the convergence of positive series. Ann. Acad. Rom. Sci., Ser. Math. Appl. 6(1), 85–99 (2014)Google Scholar
  2. 2.
    Schmelzer, T., Baillie, R.: Summing a curious, slowly convergent series quick view. Am. Math. Mon. 115(6), 525–540 (2008)MATHMathSciNetGoogle Scholar
  3. 3.
    Liflyand, E., Tikhonov, S., Zeltser, M.: Extending tests for convergence of number series. J. Math. Anal. Appl. 377(1), 194–206 (2011)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Borwein, J., Bailey, D., Girgensohn, R.: Experimentation in Mathematics: Computational Paths to Discovery. A. K. Peters, Massachusetts (2004)Google Scholar
  5. 5.
    Furstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, New Jersey (1981)MATHGoogle Scholar
  6. 6.
    Eynden, ChV: Proofs that \(\sum 1/p\) diverges. Am. Math. Mon. 87, 394–397 (1980)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Green, B., Tao, T.: The primes contain arbitrarily long arithmetic progressions. Ann. Math. 167(2), 481–547 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Hardy, G.H.: Orders of Infinity. The “Infinitärcalcül” of Paul Du Bois-Reymond. Cambridge University Press. (1910)
  9. 9.
    Knopp, K.: Theory and Application of Infinite Series. Dover Publications (1990)Google Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Abdus Salam School of Mathematical SciencesLahorePakistan
  2. 2.Department of MathematicsUniversity of CraiovaCraiovaRomania

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