hello, this is the problem:

show that

infinite

Σ sin (1/n^2) is a positive, convergent series.

n=1

Hint: use the inequality sinx is less than or equal to x for x is greater than or equal to 0

Printable View

- February 27th 2009, 12:25 AMwyhwang7Convergence of series with trigonometric function :(
hello, this is the problem:

show that

infinite

Σ sin (1/n^2) is a positive, convergent series.

n=1

Hint: use the inequality sinx is less than or equal to x for x is greater than or equal to 0 - February 27th 2009, 12:55 AMTwistedOne151p-series
Are you familiar with the convergence/divergence of the p-series ?

--Kevin C. - February 27th 2009, 01:35 AMwyhwang7
yes, but can this be applied even though the exponent is within the trigonometric function?

- February 27th 2009, 01:55 AMJameson
- February 27th 2009, 02:07 AMwyhwang7
thanks so much! but if http://www.mathhelpforum.com/math-he...7321dbc9-1.gif, wouldn't http://www.mathhelpforum.com/math-he...117f6adc-1.gif be the reverse? because n^2 would be the larger denominator

- February 27th 2009, 02:31 AMJameson
I made a typo. The sine should be around the whole expression, not just the denominator. The way I wrote it was wrong, sorry.