Riemann Sum related problems

[Jasonrich]

Hi. I'm not entirely sure that this is the appropriate section for this but I;m doing a calculus course now so I thought this may be where I need to post it. We recently started Riemann Sums and then we were given a few examples to do and I can't seem to figure this type out.

Find the sum of: ( 3*4 )+( 8*6 )+( 13*8 )+( 18*10 )+( 23*12 )+...( 98*42 )

I tried finding the sum of the product of the two series getting Σ[(5i-2)*(2i+2)] for 20 terms however I keep getting the incorrect answer - 29880 (the answers were given to us and is 25840)

If anyone could show me what I'm doing wrong, I'd appreciate it
Thanks in advance

 

[stapel]

Find the sum of: ( 3*4 )+( 8*6 )+( 13*8 )+( 18*10 )+( 23*12 )+...( 98*42 )

I tried finding the sum of the product of the two series getting Σ[(5i-2)*(2i+2)] for 20 terms however I keep getting the incorrect answer - 29880 (the answers were given to us and is 25840)

How are you arriving at your answer? Once we can see that, we'll be able to "show what you're doing wrong". Thank you!

 

[Jasonrich]

How are you arriving at your answer? Once we can see that, we'll be able to "show what you're doing wrong". Thank you!

( 3*4 )+( 8*6 )+( 13*8 )+( 18*10 )+( 23*12 )+...( 98*42 )
Σ[(5i-2)*(2i+2)]
= 10Σi^2 + 6Σi - 4n
=10[n(n+1)(2n+1)/6] + 6[n(n+1)/2] - 4(n)

For n=20 I get 29880

 

[Ishuda]

...If anyone could show me what I'm doing wrong, I'd appreciate it

I'm sorry I can't accommodate you (I happen to think you are correct).