Delhi University MCA 2020 Previous Year Questions (PYQs) – Page 2 of 4
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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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