Let f(x) = (2/4^x + 2) for real numbers x. Evaluate
f(1/2001) + f(2/2001) + ... + f(2000/2001).
To evaluate the expression f(1/2001) + f(2/2001) + ... + f(2000/2001), we need to plug in each of the given values into the function f(x) and then add up the results. Let's calculate it step by step:
Step 1: Calculate f(1/2001)
Plugging in x = 1/2001 into the given function f(x), we have:
f(1/2001) = (2/4^(1/2001) + 2)
Step 2: Calculate f(2/2001)
Plugging in x = 2/2001 into the function f(x), we have:
f(2/2001) = (2/4^(2/2001) + 2)
Repeat these steps for f(3/2001), f(4/2001), ... , f(2000/2001) and then add up all the results.
Note: The expression 4^(1/2001) represents raising 4 to the power of (1/2001).
While it may be difficult to evaluate this expression manually due to the large number of terms, you can use a computer or calculator to easily compute the values for each term and then add them together.