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 TI89 can evaluate some basic infinite
series, such as . After ( has been pasted in the entry line, enter K K ) ENTER 
You can easily solve equations using the TI89 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 TI89 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:
Here, the entry line is solve(sin(2x)=1,x)  Consult the test menu for details on how to enter inequalities and the "and". 