infinite series 2008 model test.doc

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Model Test Paper Infinite Series

1. The series 1+2+3+4+5+……………………………………..is

a. convergent b. divergent c. oscillatory d. none

2. The geometric series1+x+x²………………………..∞ is divergent

a. x ≥ 1 b. x ≤ 1 c. x = 1 d. |x| < 1

3. if lt un/vn != 0,ie. A finite value then Σun and Σvn are both

n ∞

a. convergent b. divergent c. convergent or divergent d. non

4. 1²/2 + 2²/2² + 3²/2³+…………….


5. 6-10+4+6-10+4+6-10+4……………

a. convergent b. divergent c. oscillatory d. none6. The series Σn!/n n is


7. The series α

Σ n=1 n ²/ 3n is


8. Σ1/ n n is


9. 1- 1/ 2 + 1/ 3 -1/ 4+………………is


10. a sequence {an} is said to be convergent if

lt an is

n ∞

a. finite b. infinite c .both a &b d. none

11. the series 1/e +1/e² + 1/e³ + ……………….is


12. 1/1.2 + 1/2.3 + 1/3.4 + ………………………..is


13.Σ 1/n! isa. convergent b. divergent c. oscillatory d. none

14.the series Σ(1+1/ n) ˉ n³/² is


15. 1+ 1/ 2 + 1/ 3 +1/ 4+………………is


16. 5/2 - 7/4 + 9/6 - 11/8………………… is


1




17 . in a series α

Σ n=1 1/np = 1 / 1 p + 1 / 2 p + 1 / 3 p + …………….∞, p=2,then the

series is


18.the series 1+1/2²-1/3²-1/4²+1/5²+1/6²-…………………….isa. absolute convergent b. conditionally convergent

c. oscillatory d. none

19.the series x + x²/2 + x³/3+ …………………..is diverges for

a. x<1 b. x=1 c. x>1 d. none

20.the series Σun containing positive and negative terms and it is said to be

conditionally convergent if Σun is convergent and Σ|un| is

a. convergent b. divergent c. convergent or divergent . d. none

21.if u1 - u2 + u3 - u4 + …………………….is a series of positive and negative

terms and if un >un+1 for all value of n then the series is convergent if lt un =

n ∞

a. a positive value b. a negative value c. zero d. none

22. an absolute convergent series is

a. convergent b. divergent c. convergent or divergent . d. none

23.the series 1- 1/2 + 1/3 - 1/4 +……………………….is


24.if all the term of infinite series are positive then the series is

a. convergent b. divergent c. oscillatory d. none 25.an oscillatory series should be

a. a positive series b. a negative series c. an alternating series d. none

26. if lt un = 0,then the series is

n ∞

a. convergent b. divergent c. either convergent or divergent d. none

27.if sn is the sum of the series u1 + u2 + u3 + u4 + ………………… un ,then the

series is divergent if

a. lt sn = ±∞ b. lt sn = 0 c . lt sn =a finite value d . none

n ∞ n ∞ n ∞28.if un is a series of positive terms and if

lt n(un/ un+1 -1) = k ,then Σ un diverges if

n ∞

a. k>1 b. k<1 c. k=1 d. none

2




29.the series Σ sin(1/n) is


30. if lt un1/n

= lt (1 + 2/n) n ,then the series is

n ∞ n ∞

a. convergent b. divergent c. oscillatory d. none31. Σ 3.6.9……3n 5 n

4.7.10………(3n + 1) 3n + 2


32.if sn doesnot tends to a unique limit as n ∞ then the series Σun is said

to be


33. the series 1 + 3 + 5 + 7 + 9 +……………….∞ is

a. convergent b. divergent c. oscillatory d. none34. the series Σ 1/(logn)n


35.the series Σ 1/n n is


36. the series 2- 3/2 + 4/3 - 5/4…………..is


37.the series α

Σ n=1 4n2 – n + 3

n(n2 +2)


38.1+ 1/22 + 1/32 +1/42 +…………………….is


39.lt un/ un+1 = k ,then the value of k obtained as 0.5 then the series is

n ∞


40.the series 1+ 1/2 +1/4 +1/6 +1/8 + ………………is


3

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infinite series 2008 model test.doc