Delhi University MCA Infinite Series Previous Year Questions (PYQs)
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Showing 3 questions
Which of the following is false:
(a) Every convergent positive series is convergent.
(b) Every absolutely convergent series is convergent.
(c) If the series $Σ S_n$ converges and $Σ |S_n|$ diverges, then $Σ S_n$ is conditionally convergent.
(d) The series $1 − 2^{-2} + 3^{-2} − 4^{-2} + …$ is a divergent series.
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Solution
The series
$$\sum_{n=3}^{\infty}\frac{1}{\,n(\log n)(\log\log n)^{c}\,} $$ converges if(b) c>1 (c) -1<c<0 (d) c=1
(a) 0<c<1
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Solution
If the following holds:
$ \lim_{n\to\infty}\frac{u_n}{v_n}=l,\quad u_n>0,\ v_n>0,\ l\ne 0 $ then choose the correct option:
(a) $\sum u_n$ and $\sum v_n$ converge together
(b) $\sum u_n$ diverges and $\sum v_n$ converges
(c) $\sum u_n$ converges and $\sum v_n$ diverges
(d) Neither $\sum u_n$ converges nor $\sum v_n$ diverges
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Solution
Delhi University MCA
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