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Delhi University MCA Infinite Series PYQ

Delhi University MCA PYQ
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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Delhi University MCA Previous Year PYQ Delhi University MCA DU MCA 2021 PYQ

Solution

Delhi University MCA PYQ
The series $$\sum_{n=3}^{\infty}\frac{1}{\,n(\log n)(\log\log n)^{c}\,} $$ converges if
(a) 0<c<1
(b) c>1
(c) -1<c<0
(d) c=1






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Delhi University MCA Previous Year PYQ Delhi University MCA DU MCA 2020 PYQ

Solution

Delhi University MCA PYQ

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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Delhi University MCA Previous Year PYQ Delhi University MCA DU MCA 2020 PYQ

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