How do you use the binomial series to expand (1 + x)^12?
1 Answer
Explanation:
The Binomial Theorem is a very useful tool that gives us a way to find the coefficients of binomials raised to some power
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Pascal's Triangle: This is the easiest way, but also only useful if you have a copy of the triangle on hand. If you do, look at row 12 (remember the top is row 0) and use the coefficients from that row.
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The Choose Function: This method actually comes from the theorem itself. The function basically says how many ways there are to choose
r items from a group ofn objects where order does not matter.
Turns out this function can predict binomial coefficients too. You can find them using then"C"r function on your calculator wheren=12 andr is increasing from0 -12 . -
Factorials: Should your calculator not have an
n"C"r function, you can evaluate the function directly using factorials (! ). The factorial of a whole number is that number multiply by all other whole numbers between1 and itself. The formula for the choose function is:
n"C"r = (n!)/(r!(n-r)!) wherer andn have the same meaning as before.
No matter how you get the coefficients, the answer will still be the same:
Notice how as the power of