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"!