Pascal's triangle

Get the most by viewing this topic in your current grade. Pick your course now.

Now Playing:Pascals triangle – Example 1a

Expand:
1. i) ${\left( {a + b} \right)^0}$ =
  ii) ${\left( {a + b} \right)^1}$ =
  iii) ${\left( {a + b} \right)^2}$ =
  iv) ${\left( {a + b} \right)^3}$ =
  
  Use Pascal's Triangle to expand:
  i) ${\left( {a + b} \right)^4}$ =
  ii) ${\left( {a + b} \right)^5}$ =
2. Investigating Pascal's Triangle

Pascal's Triangle - sum of numbers in each row

Row	Pattern	Corresponding binomial expression	Sum of the numbers in,the row	Express the sum as a power of 2
1	1	${\left( {a + b} \right)^0}$
2	1 1	${\left( {a + b} \right)^1}$
3	1 2 1	${\left( {a + b} \right)^2}$
4	1 3 3 1	${\left( {a + b} \right)^3}$
5	1 4 6 4 1	${\left( {a + b} \right)^4}$
:	:	:	:	:
n		${\left( {a + b} \right)^{n - 1}}$
n+1		${\left( {a + b} \right)^n}$

What is the sum of the numbers in the 10th row of Pascal's Triangle?
What is the sum of the coefficients in the expansion of ${\left( {a + b} \right)^{50}}$ ?
Express the number pattern of Pascal's triangle in "combination" form, then deduce the following formula:
$\;$ ${}_n^{}{C_0}$ + ${}_n^{}{C_1}$ + ${}_n^{}{C_2}$ + ${}_n^{}{C_3}$ + … + ${}_n^{}{C_{n - 2}}$ + ${}_n^{}{C_{n - 1}}$ + ${}_n^{}{C_n}$ = ${2^n}$

Without using a calculator, evaluate:
1. ${}_{10}^{}{C_0}$ + ${}_{10}^{}{C_1}$ + ${}_{10}^{}{C_2}$ + … + ${}_{10}^{}{C_9}$ + ${}_{10}^{}{C_{10}}$
2. ${}_5^{}{C_0}$ + ${}_5^{}{C_1}$ + ${}_5^{}{C_2}$ + ${}_5^{}{C_3}$ + ${}_5^{}{C_4}$

Now Practicing:Pascals Triangle 1b

No Javascript

It looks like you have javascript disabled.

You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work.

If you do have javascript enabled there may have been a loading error; try refreshing your browser.