Proving Bounds for a Riemann Sum: Part II

[ronho1234]

this is a riemann sum question and i need help with part 2

let Sn denote the finite sum 1+2^ 3/2 +...+n^ 3/2

i) use suitable upper and lower riemann sums for the function f(x)=x^3/2 on the interval [0,100] to prove that S99<J<100

ummm i did this and found 40000<J<41000

II) hence, or otherwise, find integer lower and upper bounds, no more than 1000 units apart, for S100

ummm i don't understand what the question is asking me...

 

[HallsofIvy]

Do you mean S99< J< S100 rather than S99< J< 100? And what is 'J'? You don't seem to have defined it anywhere.

 

[ronho1234]

yes i meant S100 and J is from the first part
Calculate J= the integral from 0-100 x^3/2dx which i found to be 40000 i think which leads onto the next two questions

 

[Bacle2]

Well, from your description, it seems you already did #2 , by finding a lower

bound of 40000 and an upper bound of 41000, since their difference satisfies

the condition.