Practice Questions for NET JRF Real Analysis Assignment: Series of Real Numbers II

Practice Questions for NET JRF Real Analysis Assignment: Series of Real Numbers

11. Consider the series 1n and 1n3/2. Then




12. If the terms of this oscillating series are grouped pairwise 322+12+23+12224+123+, then the resulting series becomes




13. Which of the following series is divergent?




14. The largest interval in which the series n=1xn converges




15. The series (221221)1+(332332)2+(443443)3+ is




16. The series x+22x22!+33x33!+44x44!+ is convergent if

17. Consider the following statements:

1. If n=1un is a series of positive terms, then the convergence of n=1(1)nun implies the convergence of n=1un.

2. If n=1un is a series of positive terms then the convergence of n=1un implies the convergence of n=1(1)nun.

3. The convergence of n=1un (un>0) implies the convergence of n=1un2.

Select the correct answer using the codes given below




18. Let the series n=1un has bounded partial series, then the series n=1unvn is convergent if the sequence {vn} is




19. If p is a real number, then the series 11p+13p+15p+17p+. to is convergent for




20. The series 11.4+12.5+13.6+. to is




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