Question

limit n tends to infinity cos(3/n) is converges sequence or diverge sequenc?

Answer 1

It diverges as 3/n converges to 0. So cos(3/n) is evaluated close to cos(0) which is 1.
Now imagine the last so many terms. They will be 1, 1, 1, 1, etc.
So the series does not converge as every time you calculate a term, you add 1 to its sum. It grows forever!

Answer 2

So, just to be clear: Its a divergent sequence

Answer 3

but our book answer says its converges to 1

Answer 4

The value of the terms converges to 1.
The series as a sum does not, because you keep adding that 1.

Im sorry, I assumed it was a series of a sum, I just work it sums more.

Answer 5

thanks dear...:)

Answer 6

limit n tend to infinity (n+1/n+3)^n the sequences is converge or diverge..?