Question about Texas Instruments TI-89 Calculator
Using elementary algebria in the binomial theorem, I expanded the power (x + y)^n into a sum involving terms in the form a x^b y^c. The coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. This is known as binomial coefficients and are none other than combinatorial numbers. Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem: The summation sign is the general term. Each term in the sum will look like that as you will see on my calculator display. Tthe first term having k = 0; then k = 1, k = 2, and so on, up to k = n.
Using binomial coefficient (n over k) allowed me to choose k elements from an n-element set. This you will see in my calculations on my Ti 89. This also allowed me to use (x+y)^n to rewrite as a product. Then I was able to combine like terms to solve for the solution as shown below.
(x+y)^6= (x+y)(x+y)(x+y)(x+y)(x+y)(x+y) = x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6
This also follows Newton's generalized binomial theorem:
Now to solve using the Ti 89.
Notice that the sum of the exponents (n ? k) + k, always equals n.
The summation being preformed on the Ti 89. The actual summation was preformed earlier. I just wanted to show the symbolic value of (n) in both calculations. All I need to do is drop the summation sign to the actual calculation and, fill in the term value (k), for each binomial coefficient.
TI-89 Titanium: I want to - oneplusgh_18.jpg
This is the zero th term. x^6, when k=0. Notice how easy the calculations will be. All I'm doing is adding 1 toTI-89 Titanium: I want to - oneplusgh_19.jpg
This is the first term or, first coefficient 6*x^5*y, when k=1.
This is the 2nd term or, 2nd coefficient 15*x^4*y^2, when TI-89 Titanium: I want to - oneplusgh_27.jpgSolution so far = x^6+6*x^5*y+15*x^4*y^2
This is the 3rd term or, 3rd coefficient TI-89 Titanium: I want to - oneplusgh_28.jpg k=3.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3
This is the 4th term or, 4th TI-89 Titanium: I want to - oneplusgh_21.jpgn> 15*x^2*y^4, when k=4.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4
This is TI-89 Titanium: I want to - oneplusgh_22.jpg 5th coefficient 6*x*y^5, when k=5.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5
TI-89 Titanium: I want to - oneplusgh_23.jpg This is the 6th term or, 6th coefficient y^6, when k=6.
Solution so far = x^6+6*x^5*y+15*x^4*y^2+20*x^3*y^3+15*x^2*y^4+6*x*y^5+y^6
Putting the coefficients together was equal or, the same as for when I used the expand command on the Ti 89.
binomial coefficient (n over k) for (x+y)^6
Using sigma notation, and factorials for the combinatorial numbers, here is the binomial theorem:
The summation sign is the general term. Each term in the sum will look like that as you will see on my calculator display. Tthe first term having k = 0; then k = 1, k = 2, and so on, up to k = n.
Posted on Jan 04, 2011
Posted on Feb 24, 2011
a 6ya expert can help you resolve that issue over the phone in a minute or two.
best thing about this new service is that you are never placed on hold and get to talk to real repairmen in the US.
the service is completely free and covers almost anything you can think of (from cars to computers, handyman, and even drones).
click here to download the app (for users in the US for now) and get all the help you need.
Posted on Jan 02, 2017
Tips for a great answer:
May 27, 2011 | Texas Instruments TI-89 Calculator
Feb 24, 2011 | Texas Instruments TI-92 Plus Calculator
The Ti 89 solves a lot of fraction problems by being in the right mode and, the use of several commands. One of my first problems here at Fixya was to find a solution for, "How do i convert a decimal answer to fractions prefferably with matrixes."
Here the problem was solved just by being in the EXACT mode.
Another fraction nightmare, so I thought was to solve for, "I want to solve a Binomial Theorem problem!" You have to go to the end of the problem but, I solved it just by the use of the expand command.
The best way to display fraction is in Pretty Print and, in the EXACT mode. Here is a small demonstration of the 3 mode setting in the Ti 89 and, the effect of each to the way a fraction is displayed.
This is a demonstration of the Ti 89 simplifying and, displaying in fractional form in the AUTO mode.
This is a demonstration of the Ti 89 making numbers proper and, displaying them in fractional form while in the EXACT mode.
This demonstration of the Ti 89 not even converting in fractional form and, displaying in the APPROX mode.
You should always use parentheses when entering equations or, fractions into the calculator. Pictured just below you can see how the Ti 89 can miss-interpret what is being entered.
The propFrac command is a great tool to reducing to the simplest form.
propFrac(expression,var). This will return an expression as a
Sometime with joining or, combining fractions you have to get the common denominator. As you can see below the comDenom command is a great tool for that.
The Ti 89's ability to compute fractions is only limited to the ability and, knowledge of the person using it. Even though, it has a tendency of making a not so, mathematically inclined person look like they have been doing them all there life.
I just gave several ways I go about solving and, displaying fractions. The best way to display fraction is in Pretty Print and, in the EXACT mode. Sometimes that isn't even enough and, you have to use parentheses and, commands to do the job.
Jan 10, 2011 | Texas Instruments TI-89 Calculator
Jun 19, 2009 | Texas Instruments TI-89 Calculator
Jun 09, 2009 | Texas Instruments TI-89 Calculator
Apr 26, 2008 | Texas Instruments TI-89 Calculator
3,471 people viewed this question
Usually answered in minutes!
Level 3 Expert
Level 3 Expert
Level 2 Expert