Im not looking for the answers, I just want to know if I am correct. Please check my work. Thankyou.
Indicate if monotonically increasing, decreasing, nonincreasing, nondecreasing or nonmonotonic.
1. { n!/2^n } = monotonically nondecreasing
2. { n^2/n^2+1 } = monotonically increasing
3. { n/2^n } = monotonically nondecreasing
4. { sin (n)/n } = monotonically decreasing
Indicate if bounded above, below, neither or both.
5. { (-1)^n e^n } = neither
6. { ((-1)^n)/n } = both
7. { n^2 } = bounded below by 1
8. { (n^2 + n + 1)/n^3 } = bounded above by 3
Indicate convergent or divergent.
9. { n^2/(n^2+1) } = converges to 1
10. { (n^2+1)/n^2 } = converges
11. { sin (n)/n }= converges by sanwiich theoreom
12. { (tan 1/n)/(1/n) } = diverges
Indicate if monotonically increasing, decreasing, nonincreasing, nondecreasing or nonmonotonic.
1. { n!/2^n } = monotonically nondecreasing
2. { n^2/n^2+1 } = monotonically increasing
3. { n/2^n } = monotonically nondecreasing
4. { sin (n)/n } = monotonically decreasing
Indicate if bounded above, below, neither or both.
5. { (-1)^n e^n } = neither
6. { ((-1)^n)/n } = both
7. { n^2 } = bounded below by 1
8. { (n^2 + n + 1)/n^3 } = bounded above by 3
Indicate convergent or divergent.
9. { n^2/(n^2+1) } = converges to 1
10. { (n^2+1)/n^2 } = converges
11. { sin (n)/n }= converges by sanwiich theoreom
12. { (tan 1/n)/(1/n) } = diverges