Convergent or Divergent

  • Thread starter realism877
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  • #1
realism877
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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?
 

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  • #2
micromass
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Evaluate the function in n=0,1,2,3,... Do you see a pattern??
 
  • #3
realism877
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I want to know how to do this algebraically
 
  • #4
micromass
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I want to know how to do this algebraically

If you follow my hint then you can do it algebraically.
 
  • #5
realism877
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It goes in increments of 180
 
  • #6
micromass
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What is [itex]n*\sin(n*\pi)[/itex] for n=1,2,3,4 ???? What is the exact result??
 
  • #7
hasan0011
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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
 
  • #8
HallsofIvy
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What? Where did you get the sum from? The question was only about the sequence.

realism877, do you not know what [itex]sin(\pi)[/itex], [itex]sin(2\pi)[/itex], [itex]sin(3\pi)[/itex], ... are? Your statement "it goes in increments of 180" implies that you do not, "[itex]\pi[/itex] 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"!
 

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