Summation formulae

1) Use summation formulae to determine the following sum (your answer will involve nn). This is complicated; carefully work it out with pencil and paper. Here nn is an unknown constant; if you are having trouble figuring out how to solve the sum, try letting n=5 and seeing how it works and then go back to using n. Note the ‘square.’

n

(2+i/n)^2 (1/n)

i=1

The sum=

Use your work from above to determine the value of the limit of this same sum.

the lmit of the sum=

2) Fill in the table of values for the given functions on the given intervals for the right-hand Riemann sum Right (n)(n). Note that the summation in the middle of the table goes with the column that follows. For the next to last column you will have to simplify Right (n)(n) by hand on paper. In the last column take the limit.

a) f(x)= x^2-3 on interval (0,3)

f(x)= 4(x-1)^3 on interval (1,3)

For these two find deltax, (xi) right end point, (f(xi)) the height, Formula for right (n), Simplified – No Sum, and Lim n goes to infinity RIght (n)