Today's soundtrack is Netherlands: Black Gaia, an album that I don't really know what to make of, but I do genuinely enjoy it. The band clearly has tons of influences; throughout the album, I heard sounds and riffs reminiscent of Ghost, High on Fire, Nine Inch Nails, Billy Talent, Devin Townsend, and Gojira. The only criticism I have of the album is that the mix sounds pretty muddy when I was listening to it in the car. Maybe that was intentional, but there was a constant low-end rumble that detracted from the clarity of the music.
This afternoon, I'm going to be learning about geometric series. This lesson builds on what I learned yesterday about geometric sequences. A geometric series, like an arithmetic series, is the sum of the terms of the sequence that it is related to. So if we have a geometric sequence whose first four terms are 2, 4, 8, and 16, its geometric series' first four terms would be 2, 6, 14, and 30 (2=2, 2+4=6, 6+8=14, and 14+16=30).
The general formula of a geometric series is Sn = t1(1-[r]ⁿ)/1-r, r≠1.
I've added a second set of brackets around the r inside of the brackets because of the way my calculator handles precedence of operators.
Helpful Hint: If a common ratio is very small with a high term number, such as r=.3 and n = 8, the result of 0.3⁸, 6.651e-5, actually means 0.00006561 - so, including the zero preceding the decimal point, there are five zeros before the number the calculator says.
To find the Sn (sum of a geometric series up to a certain term number, represented by n) of a series, we just use the general formula and solve for Sn. Sn = t1(1-[r]ⁿ)/1-r, r≠1.
To determine how many terms exist in a geometric series, we use the general formula and solve for n.