Integrating an Exponential Function

In these notes I will integrate the function y=2^x in two different ways; one by the Fundamental Theorem of Calculus, and the other by Riemann Sums. Notice that there is nothing special about the number 2. We can apply a similar integration formula to an exponential function of any base. Thanks for reading, and feel free to comment! – Jeff

Integrating an exponential function – Jeff Samuelson

Sums of Squares

A neat derivation of the sums of squares formula with  some afterthoughts at the end to keep us thinking!

Sums of Squares

Adding Permutations

I recently encountered a problem that involves the calculation of the sum of all possible 5-digit numbers that can be formed from the digits {1, 3, 5, 7, 9}; each digit can only be used once withn each arrangement.  What initially seemed to be a very daunting task was reduced to a much simpler one by resorting to some basic number theory; the solution to this problem is contained in the link directly below.

Adding Permutations

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