Convergence and Divergence of the Sequence nsin(npi)

[realism877]

I need to find out if this function is convergent or divergent when finding the limit to infiniti.

nsin(npi)

How do I solve this? Do I use the squeeze theorem or lhospital rule?

 

[micromass]

Evaluate the function in n=0,1,2,3,... Do you see a pattern??

 

[realism877]

I want to know how to do this algebraically

 

[micromass]

I want to know how to do this algebraically

If you follow my hint then you can do it algebraically.

 

[realism877]

It goes in increments of 180

 

[micromass]

What is $n*\sin(n*\pi)$ for n=1,2,3,4 ? What is the exact result??

 

[hasan0011]

I need to find out if this function is convergent or divergent when finding the limit to infiniti.

nsin(npi)

How do I solve this? Do I use the squeeze theorem or lhospital rule?

This sereis 1→∞ Ʃnsin (n∏) is equal to 1→∞ Ʃ(-1)^n (n) which is divergent hence given sereis is DIVERGENT

 

[HallsofIvy]

What? Where did you get the sum from? The question was only about the sequence.

realism877, do you not know what $sin(\pi)$, $sin(2\pi)$, $sin(3\pi)$, ... are? Your statement "it goes in increments of 180" implies that you do not, "$\pi$ radians" is the same as "180 degrees" but you should not have to convert to degrees to get this nor should you have to use a calculator. If you have taken a trigonometry or pre-calculus course you should know those "by heart"!