How do you use the convergence tests, determine whether the given series converges $\sum \frac{7 - sin (n^{2})}{n^{2}} + 1$ $sum (7-sin(n^2))/n^2+1$ from n to infinity?

Question

How do you use the convergence tests, determine whether the given series converges $\sum \frac{7 - sin (n^{2})}{n^{2}} + 1$ $sum (7-sin(n^2))/n^2+1$ from n to infinity?

2 Answers

Impact of this question

2479 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-23T14:07:38

If the general term is with the $1$ $1$ , the series is divergent, if the $1$ $1$ is not in the term, then follow me:

The function sinus has a range $[- 1, 1]$ $[-1,1]$ , so it doesn't influence the character of the series.

So:

$\frac{7 - sin (n^{2})}{n^{2}} + 1 ~ \frac{1}{n^{2}}$ $(7-sin(n^2))/n^2+1~1/n^2$ ( $~$ $~$ means asyntotic).

Since the function $\frac{1}{n^{2}}$ $1/n^2$ is convergent, so it is the given one.

Answer 2 · 2015-05-23T22:40:07

First do the limit test for convergence, and check the limit, as the limit needs to equal 0 for a series to be considered convergent, if the limit is not 0, it is then divergent.

Thus:

$lim_(n -> oo) (7 - sin(n^2))/n^2 + 1 = 0 + 1 = 1$

Therefore we can conclude that the series does not converge, and therefore is Divergent.

Science

Math

Humanities

... and beyond

How do you use the convergence tests, determine whether the given series converges $\sum \frac{7 - sin (n^{2})}{n^{2}} + 1$ $sum (7-sin(n^2))/n^2+1$ from n to infinity?

2 Answers

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you use the convergence tests, determine whether the given series converges sum (7-sin(n^2))/n^2+1∑7−sin(n2)n2+1sum (7-sin(n^2))/n^2+1 from n to infinity?

2 Answers

Related questions

Impact of this question

How do you use the convergence tests, determine whether the given series converges $\sum \frac{7 - sin (n^{2})}{n^{2}} + 1$ $sum (7-sin(n^2))/n^2+1$ from n to infinity?