Series: monotonically in/decreasing, bounded, con/divergent

shivers20

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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
 
Re: Series

shivers20 said:
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 Not


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 Not




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 Not
 
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