Unit -V
11
HOLY CROSS COLLEGE (Autonomous) TIRUCHIRAPPALLI - 620 002 II B.Sc. MATHEMATICS, SEM – III, AUGUST 2014 MAJOR CORE 4: SEQUENCES AND SERIES Subject Code : U12MA3MCT04 Unit : V Level: U Sub Unit : 5.1 Type: MCQ 1. The n th term of the series 3 1 2 2 2 + 5 3 2 4 2 + 7 5 2 6 2 +... is (a) (b) 2n−1 ( 2n+1 ) 2 ( 2n ) 2 (c) 2n +1 n 2 ( n +1 ) 2 (d) 2n−1 n 2 ( n +1 ) 2 Key:(a) 2. The n th term of the series 3 1.2 . 1 2 + 4 2.3 . 1 2 2 + 5 3.4 . 1 2 3 +... is (a) 2n+1 n ( n+1 ) . 1 2 n (b) n +2 n ( n+1 ) . 1 2 n (c) 3n n ( n+1 ) . 1 2 n (d) 2n−1 n ( n+1 ) . 1 2 n Key: (b) n +2 n ( n+1 ) . 1 2 n 3. The n th term of the series 7 1.3 . 1 5 + 11 3.5 . 1 5 2 + 15 5.7 . 1 5 3 +... is (a) n +6 n ( n+2 ) . 1 5 n (b) 7n n ( n+2 ) . 1 5 n (c) (d) n+6 ( 2n−1 )( 2n +1 ) . 1 5 n
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Transcript of Unit -V
HOLY CROSS COLLEGE (Autonomous) TIRUCHIRAPPALLI - 620 002II B.Sc. MATHEMATICS, SEM III, AUGUST 2014MAJOR CORE 4: SEQUENCES AND SERIESSubject Code : U12MA3MCT04
Unit : VLevel: U
Sub Unit : 5.1Type: MCQ
1.The nth term of the series is
(a) (b) (c) (d)
Key:(a)
2.The nth term of the series is
(a) (b) (c) (d)
Key: (b)
3.The nth term of the series is
(a) (b) (c)
(d)
Key:(c)
4.un = can be expressed as
(a) (b) (c) (d)
Key:(d)
5.un = can be expressed as
(a) (b) (c) (d)
Key: (a)
Unit : VLevel: U
Sub Unit : 5.1Type: VSA
1.Write down the nth term of the series
2.Write down the nth term of the series
3.Write the nth term of the series
4.If un = is expressed as vn vn-1, find vn.
5.If un = is expressed as vn vn-1, find vn.
Unit : VLevel: U
Sub Unit : 5.1Type: PA
1.Find the sum to n terms of the series.
2.Find the sum to n terms of the series ..
3.Sum to n terms the series .
4.Sum to n terms the series .
5.Sum to n terms the series
6.Sum to n terms the series
7.Sum to n terms the series
8.Sum to n terms the series
Unit : V
Level: U
Sub Unit : 5.1Type: E
1(a)Find the sum to n terms of the series .(7 marks)
(b)Find the sum to n terms of the series .(8 marks)
2(a)Find the sum to n terms of the series .(7 marks)
(b)Find the sum to n terms of the series (8 marks)
3(a) Find the sum to n terms of the series (7 marks)
(b)Find the sum to n terms of the series
(8 marks)
4(a)Find the sum to n terms of the series (7 marks)
(b) Find the sum to n terms of the series (8 marks)
Unit : VLevel: U
Sub Unit : 5.2Type: MCQ
1.The nth term of the series 1.2.3 + 2.3.4 + 3.4.5 + is(a) (2n 1) n (2n + 1) (b) n(n + 1) (n + 2)(c) (2n 1) 2n(2n + 1)(d) n(n 1) (n 2)Key : (b) n(n + 1) (n + 2)
2.The nth term of the series 3.5.7 + 5.7.9 + 7.9.11 + is(a) (2n + 1) (2n + 3) (2n + 5)(b) (n + 2) (n + 4) (n + 6)(c) (2n 1) (2n + 1) (2n + 3)(d) 2n (2n + 1) (2n + 3)Key : (a) (2n + 1) (2n + 3) (2n + 5)
3.The nth term of the series 1.2.3 + 4.5.6 + 7.8.9 + is(a) n(n + 1) (n + 2) (b) n(2n) (2n + 1) (c) (3n 2) (3n 1) 3n (d) (3n + 1) 3n (3n 1)Key : (c) (3n 2) (3n 1) 3n
4.The nth term of the series is
(a) (b)
(c) (d)
Key: (d)
5.The nth term of the series is
(a) (b) (c) (d)
Key: (b) Unit : VLevel: U
Sub Unit : 5.2Type: M & C
1.Match the given series with their corresponding nth term and choose the correct answer.1. 3.5.7 + 5.7.9 + 7.9.11 + A) (3n 1) (3n + 2) (3n + 5)2. 1.2.3 + 4.5.6 + 7.8.9 + B) (4n 1) (4n + 3) (4n + 7)3. 2.5.8 + 5.8.11 + 8.11.14 + C) (2n + 1) (2n + 3) (2n + 5)4. 3.7.11 + 7.11.15 + 11.15.19 + D) (4n + 1) (4n 1) (4n + 7)E) (3n 2) (3n 1) (3n)(a) 1B, 2C, 3D, 4E(b) 1C, 2E, 3B, 4A(c) 1C, 2E, 3A, 4B(d) 1C, 2D, 3E, 4BKey: (c) 1C, 2E, 3A, 4B
Unit : VLevel: U
Sub Unit : 5.2Type: VSA
1.Write the nth term of the series 1.5+2.6+3.7+.. 2.Write the nth term of the series 1.32+3.52+5.72+ ..3.Write the nth term of the series 1.2.3.4+2.3.4.5+3.4.5.6+.
4.Write the nth term of the series .
5.Write the nth term of the series .
Unit : VLevel: U
Sub Unit : 5.2Type: PA
1.Sum to n terms the series 1.2.3 + 2.3.4 + 3.4.5 + ... .2.Sum to n terms the series 3.5.7 + 5.7.9 + 7.9.11 + ... .3.Sum to n terms the series 1.3.4 + 2.4.5 + 3.5.6 + .....4.Sum to n terms the series 1.2.3.4+2.3.4.5+3.4.5.6+..5.Sum to n terms the series 4.7.10+7.10.13+10.13.16+.6.Sum to n terms the series 1.5+3.7+5.9+7.11+..7.Sum to n terms the series12.2.3+22.3.4+32.4.5+.8.Sum to n terms the series 12.2 + 22.3 + 32.4 + ... .9..Sum to n terms the series 3.7.11+7.11.15+11.15.19+..
10..Sum to n terms the series .
11.Sum to n terms the series
12.Sum to n terms the series
13.Sum to n terms the series
14.Sum to n terms the series Unit : VLevel: U
Sub Unit : 5.2Type: E
1(a)Sum to n terms of the series 2.5.8 + 5.8.11 + 8.11.14 + ... .(7 marks)
(b)Sum to n terms of the series .(8 marks)
2(a)Sum to n terms the series 1.3.5.7+3.5.7.9+5.7.9.11+.(7 marks)
(b)Sum to n terms the series (8 marks)
3(a)Sum to n terms the series 3.7.11.13+ 7.11.15.17+11.15.19.21+(7 marks)
(b) Sum to n terms the series (8 marks)4(a)Find the sum to n terms of the series 1.2.42 + 2.3.52 + 3.4.62 + ... .(7 marks)
(b)Find the sum to n terms of the series .(8 marks)
5(a)Find the sum to n terms of the series 1.3.4+2.4.5+3.5.6+..... .(7 marks)
(b)Sum the series .(8 marks)
6(a)Sum to n terms the series 1.2.3+2.3.5+3.4.7+4.5.9+.(7 marks)
(b)Find the sum to n terms of the series (8 marks)
7(a)Find the sum to n terms of the series 1.32+3.52+5.72+ ... (7 marks)
(b)Find the sum to n terms of the series (8 marks)
8(a)Sum to n terms the series 1.5 + 2.6 + 3.7 + ... .(7 marks)
(b)Sum to n terms the series (8 marks)
9(a)Sum to n terms the series 1.22 + 2.32 + 3.42 + ...(7 marks)
(b) Sum to n terms the series (8 marks)
Unit : V Level: U
Sub Unit : 5.3Type: MCQ
1.The nth term of the series is
(a) (b) (c) (d)
Key : (b)
2.If un = , vn is given by
(a) (b)
(c) (d)
Key:(c)
3.The nth term of the series is
(a) (b) (c) (d)
Key : (d)
4.The second order differences of the series 1, x, x2, x3, ... are(a) x, x2, x3(b) x 1, x2 x, x3 x2(c) (x 1)2, x(x 1)2, ...(d) 1 x, x x2, x2 x3, ...Key : (c) (x 1)2, x(x 1)2, ...5.If second difference series is a G.P. of common ratio 3 units of the form
(a) (b) (c)
(d)
Key : (b) Unit : VLevel: U
Sub Unit : 5.3Type: VSA
1.Write down the nth term of the series .
2.Write the nth term of the series .
3.Write the nth term of the series .4.Find the second order differences of the series a, ax, ax2, ax3, ... .5.If (k + 1)th difference series is a G.P. of common ratio x, give the possible form of un.
Unit : VLevel: U
Sub Unit : 5.3Type: PA
1.Find the sum to n terms of the series .
2.Find the sum to n terms of the series .
3.Find the sum to n terms of the series .
4.Find the sum to n terms of the series 5.Determine the general term of the series 4 + 14 + 30 + 52 + 80 + 114 + ... . 6.Determine the nth term of the series 10 + 11 + 14 + 21 + 34 + 55 + 86 + ... .7.Find the nth term and the sum to n terms of the series 8 + 4 + 2 + 8 + 28 + 68 + 134 + ... .8.Find the nth term and the sum to n terms of the series 1 + 4 + 11 + 26 + 57 + 120 + ... .9.Find the nth term and the sum to n terms of the series 6 + 9 + 14 + 23 + 40 ... .10.Find the nth term and the sum to n terms of the series 1+5+15+35+70+126+.... .11.Find the nth term and the sum to n terms of the series 7+10+14+20+30+48+82+.... .
Unit : VLevel: U
Sub Unit : 5.3Type: E
1(a)Find the sum to n terms and to infinity of the series . (7 marks) (b)Find the nth term and the sum to n terms of the series 6 + 3 + 2 + 3 + 6 + 11 + ... (8 marks)
2(a)Find the sum to n terms and to infinity of the series . (7 marks)(b)Find the nth term and the sum to n terms of the series 2 + 5 + 12 + 31 + 86 + 249 + ...(8 marks)
3.Find the nth term and the sum to n terms of the series (a) 1+2+3+6+17+54+171+.(7 marks) (b) 4+10+20+35+56+84+120+.(8 marks)
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