So…my next step was to determine whether this equation is true or false. This is easy enough: I could use use basic algebra to expand/factor both sides until they match.
The thing is, I’m lazy. I’d rather have a program tell me whether or not an equation is true.
Enter Sage—an open-source math library that has a python-based command-line interface. To install it on Ubuntu Linux, I simply ran:
sudo apt install sage
Once installed, you I was able to run
sage on the command line; e.g.,
~$ sage ┌─────────────────────────────────────────────────────────────┐ │ SageMath version 7.2, Release Date: 2016-05-15 │ │ Type "notebook()" for the browser-based notebook interface. │ │ Type "help()" for help. │ └─────────────────────────────────────────────────────────────┘ sage:
I entered the following, to test my equation:
k=var('k') bool( (k/2)*(3+5*k)+(5*(k+1)-1) == ((k+1)/2)*(3+5*(k+1)) )
The result was: