7/27/2019 INFINITE SERIES OBJECTIVE.doc
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INFINITE SERIES
1. The series u1 + u2 + .. is convergent if Lt un =
n (a) 0 (b) 1 (c) 1 (d) none of these
2. The series 1 / 1k + 1 / 2k+ + 1 / nk + . Is convergent if
k
(a) k > 1 (b) k < 1 (c) k = 1 (d) none of these
3. The series 1 / 1k + 1 / 2k+ + 1 / nk + . Is divergent if
k
(a) k > 1 (b) k < 1 (c) k 1 (d) none of these4. The series
1 + 2 + 3 + .. + n + .. is
(a) convergent (b) divergent (c) oscillatory (d) none
5. The series 1 + r + r2 + .. converges if
(a) |r|
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14. The series 2/12 3/22 + 4/32 5/42 + . Is
(a) conditionally convergent (b) absolutely convergent
(c) divergent (d) none of the above
15. The sum of the alternating series 1 - + - + .. is
(a) 0 (b) infinite (c) log 2 (d) none of the above
16. Let un be a series of positive terms. Given that un is
convergent and alsoltn Un + 1 / Un exists then the said limit is(a)
necessarily equal to 1 (b) necessarily greater than 1
(c) may be equal to 1 or less than 1 (d) necessarily less than
1
17. If ltnUn / Un+ 1 = k, then un converges for k(a) < 1 (b)
1 (c) > 1 (d) 1
18. The series n=1 n! / nn is
(a) convergent (b) divergent (c) oscillatory (d) none
19. The series 1 + + + . Is
(a) divergent (b) convergent (c) oscillatory (d) none
20. n=1 log ( 1 + 1/n) is
(a) convergent (b) divergent (c) oscillatory (d) none
21. If an converges and bn diverges then (an + bn)(a) converges
(b) diverges (c) oscillatory (d) none
22. nn2 / (n + 1 ) n2 is(a) convergent (b) divergent (c)
oscillatory (d) none
23. The series 1 + 2 + 3 + 4 + . Is(a) convergent (b) divergent
(c) oscillatory (d) none
24. If a1 + a2 + . Converges to s, then a2 + a3 + .. converges
to
(a) s (b) s a (c) s + a (d) none of these
25. The series 1 1 + 1 1 + .
(a) oscillates (b) converges (c) diverges none of these
