Today is our topic of discussion Infinite Series exercises-7 .
Infinite Series exercises-7
1. What is the 12th term of the series 1, 3, 5, 7,…?
1) 12
2) 13
3) 23
4) 25
2. What is the 3rd term of a sequence whose nth term=1/n(n+1)?
1) 1/3
2) 1/66
3) 1/12
4) 1/20
3. What is the 20th term of a sequence whose nth term=1-(-1)∧n?
1) 0
2) 1
3) -1
4) 2
4. The nth term of a sequence is un and un=1/n and un<10∧-4 . The value of n is
(i) n < 10³
(ii) n > 10∧4
(iii) n > 10∧4
Which one is true?
1) iii
2) i, iii
3) ii, iii
4) i, ii, iii
5. If the nth term of a sequence is un-1-(-1)xn, then its
(i) 10th term is 0
(ii) 15th term is 2
(iii) sum of first 12 terms is 12
Which one of the followings is true?
1) i, iż
2) i, iii
3) ii, iii
4) i, ii, iii
Observe the following series and answer the question (6-8) 4+4/3+4/9+…..
6. What is the 10th term of the series?
1) 4/3^10
2) 4/3^9
3) 4/3^11
4) 4/3^12
7. What is the sum of first 5 terms of the series?
1) 160/27
2) 484/81
3) 12/9
4) 20/9
8. What is the sum of the series upto infinity?
1) 0
2) 5
3) 6
4) 7
9. Find the 10th term, 15th term and rth term of the given sequences:
1) 2, 4, 6, 8, 10, 12,…
2) 1,1,2,2,2,…
3) The nth term of the sequence = 1 n(n + 1)’ ΕΝ
4) 0,1,0,1,0,1,…
5) 5, 3′ 9′ 27′ 81
6) The nth term of the sequence 1-(-1)³n 2
10. The nth term of a sequence is un 1 n
1) If un< 10-5, what will be the value of n?
2) If un> 10-5, what will be the value of n?
3) What can be said about the limiting value of un (when n is sufficiently large)?
11. Find the sum of the given series (up to infinity) if exists:
12. Find the sum of first n terms of the series given below:
1) 7+77+777+…
2) 5+55 +555+…
13. Impose a condition on x under which the infinite series 1/(x+1)+1/(x+1)²+1/(x+1)³+ ……. will have a sum (to infinity) and find that sum.
14. Express each of the given repeating decimals as a rational fraction:
1)0.27
2) 2.305
3) 0.0123
4) 3.0403
15. a+ab+ab²+… is a geometric series.
1) What is the 7th term of the series?
2) If a = 1 and b = 1/2 ; determine the sum to infinity of the series if exists.
3) Determine the sum of first n terms of the series which is found by placing 3 in stead of a, 33 in stead of ab and 333 in stead of ab².
16. The sum of three consequent terms of a geometric series is 24×4/5 multiplication is 64. and
1) Construct two equations based on the given information.
2) Determine the first term and the common ratio.
3) If the common ratio is 1/5 then determine the sum to infinity of the series.
17. There are four dogs standing in the four corners of a square area, each side of which is 1 km. Now, every dog runs blindly towards the dog on its right in the same velocity, covering half the distance. After opening the eyes, they run similarly to the dog on its right again, covering half the distance.
1) If they continue to run like this, what will be the terminal position of the dogs? How much distance each will eross?
2) Answer the previous question if after covering half the distance, without changing direction each dog covers additional 1/k times of the distance and then changes direction.
3) Answer both the questions stated above if the area was not a square, rather an equilateral triangle.
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