Sequences and Series

Alexeia

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Joined
Mar 24, 2015
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5
Hi,

Please help me with this question: Investigate the convergence of the sequence tanx;tan2x;tan3x;........;tannx for xE(-90;90 degrees). Steps to follow: Find common ratio. Draw the graph. For which values of x will this sequence converge. Determine sum to infinity.

I did try to solve, but file type too big to upload my answers.

Please help..

Thanks
 
Hi,

Please help me with this question: Investigate the convergence of the sequence tanx;tan2x;tan3x;........;tannx for xE(-90;90 degrees). Steps to follow: Find common ratio. Draw the graph. For which values of x will this sequence converge. Determine sum to infinity.

I did try to solve, but file type too big to upload my answers.

Please help..

Thanks
Call the common ratio r. If you have a sequence r, r2, r3, ..., rn what is the limit as n goes to infinity if \(\displaystyle -1\, \lt\, r\, \lt\, 1\)? Is there a limit if r=-1 and, if so, what is it? Is there a limit if r=1 and, if so, what is it? What is the limit if \(\displaystyle r\, \lt\, -1\, or\, 1\, \lt\, r\)?

What does the ratio test for the series sum tell you?
 
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