Maths - Series
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Flashcards
2021-09-18
What’s the format of a general arithmetic sequence term $U _ n$ for common difference $d$ and start term $a$?
\[U_n = (n - 1)d + a\]
What’s the formula for the sum $S _ n$ up to term $n$ of a sequence with start $a$ and common difference $d$?
\[S_n = \frac{n}{2}\left( (n - 1)d + 2a \right)\]
What’s the formula for the sum $S _ n$ of an arithmetic sequence between terms $a$ and $l$?
\[S_n = \frac{n}{2}\left( a + l \right)\]
What does it mean for a geometric sequence to be divergent?
The terms get further and further apart.
What does it mean for a geometric sequence to be convergent?
The terms get closer and closer together.
What must be true about $r$ for a convergent geometric series?
\[|r| < 1\]
What must be true about $r$ for a divergent geometric series?
\[|r| > 1\]
2021-10-03
What is the formula for the sum of a convergent geometric sequence with $ \vert r \vert < 1$?
\[\frac{a}{1 - r}\]