Microsoft Word - c9hw.pdf 1. Write the first three terms of the sequence. 3. The formula for the nth term an of a sequence {an } is given below. Find the values of a1 , a2 , a3, and a4. 4. The first...

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Microsoft Word - c9hw.pdf 1. Write the first three terms of the sequence. 3. The formula for the nth term an of a sequence {an } is given below. Find the values of a1 , a2 , a3, and a4. 4. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. a = n 4 n 4 n + 2 ( Type an integer or a simplified fraction.) a 1 = ( Type an integer or a simplified fraction.) a 2 = ( Type an integer or a simplified fraction.) a 3 = Type ( an integer or a simplified fraction.) a 4 = 2. a = n n + 4 The first three terms are , , and . a 1 = a 2 = a 3 = ( Simplify your answers. Type integers or fractions.) A formula is given below for the term of a sequence . Find the values of , , , and . n t h a n a n a 1 a 2 a 3 a 4 n + 1 a n = ( Type an integer or a fraction.) a 1 = Type ( an integer or a fraction.) a 2 = ( Type an integer or a fraction.) a 3 = ( Type an integer or a fraction.) a 4 = 5. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. 6. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. a 1 , a n / (1 n ) = 8 a n + 1 = + 2 a 1 = a 2 Simplify ( your answer.) = a 3 Simplify ( your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 Simplify ( your answer.) = a 8 ( Simplify your answer.) = a 9 ( Simplify your answer.) = a 10 Simplify ( your answer.) = a 1 , ( 1) a n / = 1 0 a n + 1 = − n + 1 5 a 1 = a 2 Simplify ( your answer.) = a 3 ( Simplify your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 ( Simplify your answer.) = a 8 ( Simplify your answer.) = a 9 ( Simplify your answer.) = a 10 Simplify ( your answer.) = . 8. Find a formula for the nth term of the sequence. − 2, 1, 6, 13, 22, ... Determine the sequence's formula in terms of n. an = , n ≥ 1 9. Find a formula for the nth term of the sequence where an is calculated directly from the value of n. 2 , 6 , 10 , 14, 18, ... 10. Find a formula for the nth term of the sequence where an is calculated directly from n. . 11. Determine if the sequence {an } converges or diverges. Find the limit if the sequence converges. n an = 3 + (0.3) 7. a = 2 , a = 1 n + 1 n a n n + 3 a = 1 Simplify ( your answer.) a = 2 ( Simplify your answer.) a = 3 ( Simplify your answer.) a = 4 ( Simplify your answer.) a = 5 ( Simplify your answer.) a = 6 ( Simplify your answer.) a = 7 ( Simplify your answer.) a = 8 ( Simplify your answer.) a = 9 ( Simplify your answer.) a = 1 0 Find a formula for the nth term of the sequence in terms of n. for a n = n ≥ 1 , a n = n ≥ 1 for a n = n ≥ 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 12. Determine whether the following sequence converges or diverges. If it converges, find its limit. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. an = n + 5 14. The formula for the nth term an of a sequence {an } is given below. Find the values of a1 , a2 , a3, and a4. 15. The first term of a sequence along with a recursion formula for the remaining terms is given below. Write out the first ten terms of the sequence. A. The sequence converges, and . ( Simplify your answer.) a l i m n n = B. The sequence diverges. { } a n = 8 n + ( − 1 ) n 8 n 13. A. The sequence converges to . ( Simplify your answer.) a = l i m n n B. The sequence diverges. Write the first three terms of the sequence. The first three terms are , , and . a 1 = a 2 = a 3 = ( Simplify your answers. Type integers or fractions.) a = n 3 n 3 n + 3 ( Type an integer or a simplified fraction.) a 1 = ( Type an integer or a simplified fraction.) a 2 = ( Type an integer or a simplified fraction.) a 3 = Type ( an integer or a simplified fraction.) a 4 = 16. Find the first 4 terms and the eighth term of the recursively defined sequence. c1 = 7, c2 = − 3 , and ck + 2 = ck + ck + 1 , for k ≥ 1 The first term is (Simplify your answer.) The second term is . (Simplify your answer.) The third term is . (Simplify your answer.) The fourth term is . (Simplify your answer.) . 17. Find a formula for the nth term of the sequence in terms of n. . 18. Find a formula for the nth term of the sequence where an is calculated directly from n. a 1 , ( 1) a n / = 8 a n + 1 = − n − 1 2 a 1 = a 2 Simplify ( your answer.) = a 3 ( Simplify your answer.) = a 4 ( Simplify your answer.) = a 5 ( Simplify your answer.) = a 6 ( Simplify your answer.) = a 7 ( Simplify your answer.) = a 8 ( Simplify your answer.) = a 9 Simplify ( your answer.) = a 10 Simplify ( your answer.) = . The eighth term is ( Simplify your answer.) for a n = n ≥ 1 . 19. Determine if the sequence {an } converges or diverges. Find the limit if the sequence converges. Select the correct choice below and fill in any answer boxes within your choice. 20. Does the sequence {an } converge or diverge? Find the limit if the sequence is convergent. Select the correct choice below and, if necessary, fill in the answer box to complete the choice. 21. Does the sequence {an } converge or diverge? Find the limit if
Answered 1 days AfterJun 15, 2021

Answer To: Microsoft Word - c9hw.pdf 1. Write the first three terms of the sequence. 3. The formula for the nth...

Sayantan answered on Jun 17 2021
141 Votes
Maths answers:
6. a1= 0, a2= ½, a3= 1/5, a4= 1/10, a5= 2/35, a6= 1/28, a7= 1/42, a8= 1/60, a9= 2/165, a10= 1/110
7.
8.
9.
10.
11. a. Limit converges and
12. B
13. 1
/8, 4/14/ 11/32
14. a1= a2= a3= a4= 1/27
15. a1= 8, a2= 4, a3= -2, a4=-1, a5= +1/2, a6= ¼, a7= -1/8, a8= -1/16, a9= 1/32, a10= 1/64
16. First term is 7, second term is -3, third term = 4, fourth term = 7, eighth term= 47
17.
18.
19. option A, value is
20. Converges. Value is
21. Converges at
22. converges at
23. infinity
24.
25.
26. option B. non decreasing function having a greatest lower value of 1
27. option A. greatest lower bound of x1 and least upper bound of 0.
28. first part ans: B, Maximum value of for any n is equal to 1. Second part answer: C
29. x1= 2, x2=1.75, x3=1.732142857, 4=1.7320508, x5= 1.732050808,
x6= 1.732050808. the approximated value taken here is
30.
First 25 terms are:
    n
    nsin(1/n)
    1
    0.841470985
    2
    0.958851077
    3
    0.98158409
    4
    0.989615837
    5
    0.993346654
    6
    0.995376796
    7
    0.996602109
    8
    0.997397867
    9
    0.997943657
    10
    0.998334166
    11
    0.998623159
    12
    0.998842994
    13
    0.999014098
    14
    0.999149877
    15
    0.999259424
    16
    0.999349085
    17
    0.999423398
    18
    0.999485676
    19
    0.999538383
    20
    0.999583385
    21
    0.999622114
    22
    0.999655683
    23
    0.99968497
    24
    0.999710673
    25
    0.999733355
The sequence appears bounded from above and below (C)
The sequence is converging. Appears to converge
Value of L is 1.
31. formula for partial sum is
Series converges sum is 10
32. . Series is convergent, series sum is 5.
33.
    a1
    0.6
    a2
    1.72
    a3
    1.944
    a4
    1.9888
    a5
    1.99776
    a6
    1.999552
    a7
    1.9999104
    a8
    1.99998208
Series converges and sum = 2
34....
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