Further Maths - Series
Series
Core 1
- Further Maths - Sums of Natural NumbersA
- Further Maths - Sums of SquaresA
- Further Maths - Sums of CubesA
- Further Maths - Series Tips and TricksA
- Further Maths - Induction for SeriesA
Core 2
Flashcards
What is the notation for series?
- Sigma notation
- e.g. $\sum^{n} _ {r = 1} n$
What sequence does $\sum^{n} _ {r = 1} (3r - 1)$ describe?
How can you find the sum of a series that starts at $r = k$?
How can you rewrite $\sum^{n} _ {r=k}$?
What is $\sum^{n} _ {r=1} f(r) - \sum^{k-1} _ {r=1} f(r)$ equivalent to?
How can you rewrite $\sum^{n} _ {r=1} kf(r)$?
What’s an alternate form of $k \times \sum^{n} _ {r=1} f(r)$?
How could you rewrite $\sum^{n} _ {r = 1} (f(r) + g(r))$?
How could you rewrite $\sum^{25} _ {r=1} (3r + 1)$?
How can you find the sum of a series that starts at $k$, not $1$?
What’s another way of writing $\sum^{n} _ {r=k}$?
How do you deal with something other than $n$ at the top of the $\Sigma$, like $\sum^{4n-1} _ {r=1}$?
Instead of substituting $n$, you subsititue $4n-1$ into the formula.
If you show $\sum^{4n-1} _ {r=1} (3r+1) = 24n^2 - 2n - 1$, what’s the first step to solving $\sum^{7} _ {r=1} (3r+1)$?
First solve:
\[4n - 1 = 7 4n = 8 n = 2\]If $\sum^{n} _ {r=1}$ is linear, the expression for $\sum^{n} _ {r=1} r$ is…?
Quadratic.
If $\sum^{n} _ {r=1}$ is linear, the expression for $\sum^{n} _ {r=1} r^2$ is…?
Cubic.
If $\sum^{n} _ {r=1}$ is linear, the expression for $\sum^{n} _ {r=1} r^3$ is…?
Quartic.