MrSilvers

Yes that's it. It's in the half angle section of the book. It's trig for dummies by Mary Jane Sterling. I just wondered about the breakdown of the simplified sum with the 4 in the denominator and whether the 4 came from using it as an LCD. 

Sorry hectictar it's the way i wrote it out, it's wrong. It should be a square root then under the square root is 2/2 - sq root of 3/2 that's all in the numerator of the fraction. Then the 2 is in the denominator. That simplifies to the second sum i wrote but the second sum also is under a sq root. I omitted both of those roots in my post.  It's hard to write it out on here. Does that make more sense now? Sorry.

Thanks for all the help mate it's appreciated. I wanted to give your posts the thumbs up but i'll have to wait until i can reset my password to get into my account. I'm glad i came back on and made a new account on the forum as i see me having a lot of questions from this calculus book!

  Gary

Thanks mate. Yeah i'm wondering about the whole sum apart from the first line!  That bit where he wrote that about not showing all the work really freaked me out and i'm saying: "But it's a dummies book! You're supposed to be explaining everything, every step."  I have two Algebra books I and II by Mary Jane Sterling in the dummies series and she explains everything a lot better and doesn't leave anything out.  I was going to ask how he got from the three 6's in the denominators to the 3 2 in the next line but looking at it i take it he's just divided but in like the opposite direction using the 2 and 3 in the numerators into 6?  I forgot you could do that and am so brainwashed into just dividing the standard way.  Yeah i think the author was being a bit lazy and trying to save himself some work in explaining how he derived each line in the sum!

  Gary

Thanks so much hectictar i appreciate it. That's the exact bit i'm talking about. I looked at your post and saw it and said "That's it!"  Your post helps me out a lot.  I wonder why he didn't explain it all out in the book?  I thought that was the idea for the dummies books to completely break things down in easily understood language as Calculus can get complicated. Thanks again.

  Gary

Hi mate, thanks. It's a Riemann sum or at least in that section of the book  and it's for calculating the area under a curve so it's integration. I'll try to write it out here, the first line of it anyway. He starts off with using the sigma summation sign and then on the next page he uses the integration sign and takes it to the limit of the function. I think basically he then takes the limit as infinity in order to get the exact area under the curve. 

27/n^{3 .}  n(n+1)(2n+1)/6 +  3.n/n   

That's the basic sum. The last bit is 3 times ndivided by n. The dot for multiplication is hard to see but i didn't want to use an x because it can cause confusion.  Now the second line in the book has a breakdown of the middle bit there, the n+1 bit, where he gets n3/3 + n²/2 + n/6 but that's the bit where he writes at the side that he didn't include all his work. So it's not broken down how he gets there and for a beginner it's just impossible trying to figure it out. I've looked on YT videos for the sum of the squares that the middle part of the sum concerns but most go into proving the theory or induction or something which is way above my head and too advanced for me. I'm just looking for a kind of simple breakdown if it's possible.  I think he omitted the explanation because he didn't want to have to write all the extra steps out!!

  Gary