l>Summations top top the Graphing Calculators
 MATH 202 FALL 2002
Evaluating Sumswith Graphing CalculatorsHere are some examples showing just how to usage the TI-83 Plus, the TI-85,and the TI-89 to evaluate the kinds of sums that come up in numericalintegration and collection approximations of functions.We will work out two instances on every of the three calculators. First is a an easy summation the 1/k2 for kgoing from 1 to 20. In symbols, The 2nd is a contempt more complex sum in i beg your pardon the an ext natural index is no i, however (1 +(i/5)). In this example, we will certainly take benefit of the factthat we are actually adding up the values of the duty e-x2 as the change xtakes on the values 1.2, 1.4, 1.6, 1.8, ..., 2.8, 3.0.Click on the appropriate link to jump to the example using theTI-83 Plus,theTI-85,or theTI-89.On the TI-83 Plus,we usage the sum( and seq( functions. Thesum( command is found under LIST, MATH. Toget there us press<2nd> LISTand then touch the right arrowkey double to highlight MATH. The sum( command isselection 5 top top the result list. Theseq( command is found under LIST, OPS. Toget there us press<2nd> list again,and climate touch the right arrowhead once to to mark OPS.The seq( command is again selection 5.Back top top the home screen, we have actually the display and we"re prepared to crucial in the details of the an initial example. We wantto add up the expression 1/k2 for k goingfrom 1 come 20. We use the miscellaneous alpha and numeric tricks to completethe line as shown below. Us then press and also wait because that the answer to appear.Here"s what we get: We review the input line together "the amount of the succession 1/k2as k goes native 1 to 20 by ones." That"s what the last "1" is:the increment.As discussed above, we may treat the 2nd example together the sum ofe-x2where x takes on the values 1.2, 1.4, 1.6, ..., 2.8, 3.0. Thatis, x goes native 1.2 to 3.0 in procedures of 0.2.Using the sum( and seq( regulates as before, we keyin the complete summation command and also then press. We get On the TI-85,we usage the sum( and also seq( functions,which are located on the perform OPS menu. To getthere, we press<2nd> and then to choose the OPSmenu. We then push to get to the part of the food selection that weactually want.Finally, pressing reasons the command stringsum seq( to show up in the algebra window.For the very first example, we want the sum of the expresion1/k2 as k goes from 1 to 20. We an essential this inusing the miscellaneous alpha and numeric keys, and then press and also wait for an answer. Us getsomething favor this: We check out the input line as "the sum of the sequence 1/k2as k goes native 1 to 20 through ones." That"s what that last "1" is:the increment.As discussed above, we might treat the second example together the amount ofe-x2where x bring away on the values 1.2, 1.4, 1.6, ..., 2.8, 3.0. Thatis, x goes indigenous 1.2 come 3.0 in actions of 0.2.Using the sum and also seq( regulates from the list OPS menu, we crucial inin the complete summation command and then press. We get On the TI-89,there is a summation command (it reflects up together a resources sigma) underthe top-level Calc menu, however this turns out no to it is in asflexible together the sum( and seq( commands hiding underthe MATH list menu.In these examples, we will certainly usesum( and seq(.To uncover them, us press<2nd> $and then <3> to select the list menu. We press <6> to pick sum\left(so the "sum\left(" appears in the input line\right), and then walk backthrough the regimen again:<2nd><3> and also finally <1> to pick seq\left(.To finish the an initial example, we crucial in the debates tosum\left(seq\left(, so the the input line looks likesum\left(seq\left(1/k^2,k,1,20,1\right)\right)This reads "the amount of 1/k2 together k goes indigenous 1to 20 through ones." the last "1" prior to the parentheses is the incrementvalue. We push, and also the calculator display screen shows united state apretty-print version of the sum-sequence us asked for, along with theexact answer:$ This could not it is in the many useful form for the answer; if we prefer adecimal approximation, we have the right to request one by pushing the greendiamond crucial and then again.We get As discussed above, we may treat the 2nd example as the amount ofe-x2where x bring away on the worths 1.2, 1.4, 1.6, ..., 2.8, 3.0. Thatis, x goes from 1.2 to 3.0 in procedures of 0.2.This time we"ll usage the increment attribute of the seq(command. To begin, we run through the menus together before, with<2nd> $<3> <6> <2nd><3> <1> tobring up sum\left(seq\left(. This time we an essential in the arguments toseq\left( using the variable x.$

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The input heat readssum(seq(e^(-x^2),x,1.2,3,0.2))We press and again the calculatorshows united state a pretty-print variation of the amount we asked for, and then theanswer. This time, the price is given as a decimal approximationbecause we used decimal notation in the input line.We remark the if we had avoided decimals in the input line, say, bykeying in sum(seq(e^(-x^2),x,6/5,3,1/5))then the calculator would certainly have provided us an exact answer -- somehorrible chaos with several e"s in it -- and we would certainly haveneeded come ask the green diamond for assist once again. 