- #1
Sabricd
- 27
- 0
Hello,
I have to determine whether the given series diverges or converges. [tex]\sum[/tex] cos(n*pi)/(n^(3/4)) where n= 1 and goes to infinity.
I tried a couple numbers for n and got:
-1 + 1/(2)^(3/4) - 1/(3)^(3/4)
Hence I came up with the series: [tex]\sum[/tex]((-1)^n)/(n)^(3/4) where n=1 and goes to infinity.
I guess my main question is that now that I have that new representation of the series, why can't I just take the absolute value of the series and say that it is a p series with p< 1 and therefore diverges.
My book took the limit of the series and got 0 and said it converged. Why can't you use the p-series test?
Thank you,
I have to determine whether the given series diverges or converges. [tex]\sum[/tex] cos(n*pi)/(n^(3/4)) where n= 1 and goes to infinity.
I tried a couple numbers for n and got:
-1 + 1/(2)^(3/4) - 1/(3)^(3/4)
Hence I came up with the series: [tex]\sum[/tex]((-1)^n)/(n)^(3/4) where n=1 and goes to infinity.
I guess my main question is that now that I have that new representation of the series, why can't I just take the absolute value of the series and say that it is a p series with p< 1 and therefore diverges.
My book took the limit of the series and got 0 and said it converged. Why can't you use the p-series test?
Thank you,