Sigma Notation (Edexcel IGCSE Further Pure Maths): Revision Note

• Your calculator may be able to use sigma notation

  • If so make sure you know how it works 

  • You can use this to check your work

The terms of a series are defined by  $u_n=2\times 3^{n-1}$,  for  $n=1,2,3,...$ . 

(a) Write an expression for the sum of the first six terms of the series using sigma notation.

Use sum limits from 1 to 6

$\sum _{k=1}^6{u}_k$

Note that '$n$' is replaced by '$k$' to match the variable used for the sigma sum

Now replace $u_k$ with the actual formula, being sure to use $k$ instead of $n$ again

$\mathbf{\sum }_{\mathbf{k}\mathbf{=}\mathbf{1}}^{\mathbf{6}}\left(2\times 3^{k-1}\right)$

(b) Write an expression for the sum of the seventh through twelfth terms of the series using sigma notation.

This will be the same as in part (a), except that the limits will be 7 on the bottom and 12 on the top

$\mathbf{\sum }_{\mathbf{k}\mathbf{=}\mathbf{7}}^{\mathbf{12}}\left(2\times 3^{k-1}\right)$

(c) Write an expression for the sum of the first $n$ terms of the series using sigma notation.

This is very similar to the above, but the sum limits will start at 1 and go to $n$

$\sum _{k=1}^n{u}_k$

Be careful here  –  $k$ is the variable for the sigma sum, and $n$ means we're going up to the $n$^th term

$\mathbf{\sum }_{\mathbf{k}\mathbf{=}\mathbf{1}}^{\mathbf{n}}\left(2\times 3^{k-1}\right)$