cmi-entrance 2013 QA12

cmi-entrance · India · pgmath 4 marks Sequences and Series Convergence/Divergence Determination of Numerical Series

The series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ where $a _ { n } = ( - 1 ) ^ { n + 1 } n ^ { 4 } e ^ { - n ^ { 2 } }$
(a) has unbounded partial sums;
(b) is absolutely convergent;
(c) is convergent but not absolutely convergent;
(d) is not convergent, but partial sums oscillate between $-1$ and $+1$.

The series $\sum _ { n = 1 } ^ { \infty } a _ { n }$ where $a _ { n } = ( - 1 ) ^ { n + 1 } n ^ { 4 } e ^ { - n ^ { 2 } }$\\
(a) has unbounded partial sums;\\
(b) is absolutely convergent;\\
(c) is convergent but not absolutely convergent;\\
(d) is not convergent, but partial sums oscillate between $-1$ and $+1$.

Paper Questions

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