Hmm not sure if I copied that image properly. Anyways I'm really confused on what exactly I need to do. The question is related to an introduction to calculus course. Where you take an infinite number of sqaures to find the area under the curve. For example taking the right hand side of the subinterval, where you multiply 1/n and (1/n)^2 and keep adding until 1/n.(n/n)^2. which would solve to be (1/n)^3 [1^2 + 2^2 + 3^2 + ... + n^2].
However 1^2 + 2^2 + 3^2 + ... + n^2 = ( n(n+1) (2n+1) )/ 6 <-- not sure where this formula comes from
Then you multiply that by 1/n^3 then take the limit as n approaches infinity solve using l hospitals rule and you get 1/3 for the area for the right hand side
But the question i have to solve is 1^15 + 2^15. etc where do i find the formula for 1^15, or better yet, how do i work it out? and how does it relate to 1/n^15, 1/n^16, 1/n^17 from the question. Im so confused Thanks so much for any tips you guys can see