Question

need help with algebra 2 sigma notation and geometric series. thank you

Answer 1

need help with sigma notation. thank you i'm home schooled and could use help.

Answer 2

whats the issue?

Answer 3

could use some help with these i'm home schooled and don't know how to do these i tryied on my own but failed..thanks

Answer 4

i wish i had sufficient time to go over these right now, but ill have to look at it better tomorrow. good luck

Answer 5

there is the long method, which tends to give proof to the formula

take that 4*6^(n-1)

\[4(6^0)+4(6^1)+4(6^2)+4(6^3)+4(6^4)+...\]
\[4(6^0+6^1+6^2+6^3+6^4+...)\]
now all there is to worry about is that geometric part in base 6

Let:\[~~~~~~A=(6^0+6^1+6^2+6^3+6^4+~~...+~~~~6^{n-1})\\-6A=(~~~~-6^1-6^2-6^3-6^4-6^5-...-6^{n-1}-6^n)\\-----------------------\\(1-6)A=6^0+0+0+0+0+..................-6^n\]
\[A=\frac{1-6^n}{1-6}\]
\[4A=\lim_{n\to \infty}\frac{4(1-6^n)}{1-6}\]our main issue here is that 6^n part, as n gets bigger and bigger, 6^n gets endlessly bigger and bigger. Whenever we have a common ratio that is bigger than 1, we cant sum it up.