The squence is 1 + 4 + 16 + 64+ ... + 4^n. I know the common ratio is 4, and to use ((r^n) -1)/(r-1) but i'm confused about n since the problem also states that n >= 0. Does that mean the sequence starts at index 0? Meaning f(0) = 1? If so, that would mean the sum of the n terms is = to 4^n? So the equation would be ((4^n+1)-1)/(4-1)?
Hello, i'm trying to figure out how my professor wants me to solve this geometric series problem.
The squence is 1 + 4 + 16 + 64+ ... + 4^n. I know the common ratio is 4, and to use ((r^n) -1)/(r-1) but i'm confused about n since the problem also states that n >= 0. Does that mean the sequence starts at index 0? Meaning f(0) = 1?
If so, that would mean the sum of the n terms is = to 4^n? So the equation would be ((4^n+1)-1)/(4-1)?
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So the problem stating n >= 0 doesn't mean anything? Or is that where the +1 comes from? If it says n >= 1 so that make n just n instead of n + 1? I'm probably overthinking it, as is one of my bad habits. However, if I say n is 1, 4^1-1/3 = 1 but if I try 4^1+1-1/3 I get 4^2-1/3= 15/3 = 5, which is not the sum of the first number in the sequence alone. Thanks so much.
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