I think I've got an answer from another responder. His post is below:
For this sum you can just plug in the values until you hit 20. That's all you need to do.
10+11+12+13+14+15+16+17+18+19+20 = 165
His way is unnecessary and requires much more work. A better way is this, when ever you...
How do I evaluate the sum of this sigma notation problem?
20
∑ k
k=10
Normally, I would think to use the theorem for the sum of the first n integers:
n
∑ k = n(n+1)/2
k=1
I don't know how to do this, however, since the lower limit is k=10, not k=1.
My professor wrote this note on the board...
Homework Statement
What are the critical points of function f(x) = 2 (x^2 + 4)^(1/2) - 4x + 24 ?Homework Equations
When f'(x) equals 0 or is undefined, x is a critical number.The Attempt at a Solution
The original function is f(x) = 2 (x^2 + 4)^(1/2) - 4x + 24 .
I got the derivative as f'(x) =...