Summation


From the home screen, press to access the Calc menu. Then press to select 4:( sum. One can then evaluate finite sums and some infinite series. To evaluate a summation, apply the syntax

(summand, index of summation, lower index of summation, upper index of summation).

For example, to evaluate , after ( has been pasted in the entry line, enter

One may also use the alpha key to enter the index as i or k as used more often in summation notation. For example, to compute the sum of as k goes from 1 to 100, first select 4:( sum from the Calc menu. Then, after ( has been pasted in the entry line, enter

K K

To evaluate , after ( has been pasted in the entry line, enter

K K N

The TI-89 can evaluate some basic infinite series, such as . After ( has been pasted in the entry line, enter

K K ) ENTER

Solve

You can easily solve equations using the TI-89 graphing calculator. The key decision for user is whether to work in the real or the complex number system. For example, let's solve the quadratic equation, .

To solve the equation in the real number system, press F2 to select the algebra menu, press 1 to select 1:solve(, enter the equation, then press , (comma) X ) ENTER. The TI-89 responds with the answer false, indicating that this equation has no real roots.

To obtain the complex roots, follow the above procedure with the following exception. Instead of selecting 1:solve( , select A:Complex , then select 1:cSolve. The complex roots are

In particular, note that the option 1:solve yields solutions only in the real number system; whereas, cSolve yields solutions in the complex number system.

You may also solve an equation with a constraint. This is handy, for example, in solving trigonometric equations. For example, letŐs solve ) = 1 for . The appropriate syntax is:

solve(equation,variable) | constraint.

Here, the entry line is

solve(sin(2x)=1,x) |

Consult the test menu for details on how to enter inequalities and the "and".