okay i finally understand what you meant. The product symbol, okay I figured it out. So if you work out the series, you get 1/2*3/5*5/8*7/9 ... (2i-1)/(3i-1). You end up with the original question. So, now what?
Okay I understand what you mean. However, I've never used that product symbol (it looks like the pi symbol when you type it) in calculus so you please explain briefly by what that indicates? I have indeed used i=1 though.
Yes sorry about the negative sign. I meant (n-1)^3/2. I used the integral test and this series converges. I compared this series to the original and the series will converge overall. This problem is resolved.
Sorry, but can you just specify what you mean by "the product"? That is what is...
First, I don't understand where you got the (n-1)^3/2 from. I want to compare the original series with 1/n(n-1)^1/2. First I have to prove that 1/n(n-1)^1/2 converges/diverges and then use the comparasion test to show that 1/n(n-1)^1/2 is greater than the orginial series which means that the...
for the first question, I am starting to understand what you are getting at. But for the comparasion test, is it important to show whether the series I am comparing the original to converges or diverges. Since, 1/n square root (n-1) is greater than 2/..., the series will converge, but I am...
So for the first question, if you plug in n=3, then 1/n*square root (n-1) is not greater than the other inequality but it is less than. So, I am thinking wouldn't the < be the other way around?
Using the comparasion test, I could compare 2/... with 1/n*square root of (n-1). So therefore the...
Question:
For c>0, the graphs of y=(c^2)(x^2) and y=c bound a plane region. Revolve this region about the horizontal line y= -(1/c) to form a solid.
For what value of c is the volume of this solid a maximal or minimal (Use calculus 1 techniques).
First, I found the volume of this...
For the first question, I don't understand how you got (n-1)^1/2 + (n+1)^1/2 < 2(n-1)^1/2. I know how to use the comparasion test but I am not sure what to compare the series with, since the numerator is complicated and the denominator is just n.
Would the ratio test work on this series. a_n+1...
1) Determine whether the series converges or diverges: summation from n=1 to ∞ of (square root of (n+1) - square root of (n-1)) / n. clearly state which test you are using.
2) Determine whether the series converges or diverges: summation from n=1 to ∞ of (1*3*5*... (2n-1)) / (2*5*8*...
1) Determine whether the series converges or diverges: summation from n=1 to ∞ of (square root of (n+1) - square root of (n-1)) / n. clearly state which test you are using.
2) Determine whether the series converges or diverges: summation from n=1 to ∞ of (1*3*5*... (2n-1)) / (2*5*8*...