hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
hvvrq $ulwkphwlf 6htxhqfhv dqg 6hulhv - NCPN
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a<br />
S <br />
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R.E.A.C.T. Strategy<br />
Experiencing<br />
<br />
<br />
805 ( . ) + 1 <br />
=<br />
1<br />
<br />
∞<br />
∑<br />
<br />
Have students calculate the area under the curve formed by the parabola<br />
y = –x 2 + 9 and the x-axis. Instruct students to accomplish this by drawing a<br />
series of circumscribed rectangles under the curve and computing the area of<br />
each of these rectangles. Ask students how the size of the rectangle will affect<br />
the approximation of the area under a curve.<br />
LESSON PLANNING<br />
Vocabulary<br />
infinite geometric series<br />
converges<br />
diverges<br />
point of discontinuity<br />
asymptote<br />
Extra Resources<br />
Reteaching 9.4<br />
Extra Practice 9.4<br />
Assignment<br />
In-class practice: 1–5<br />
Homework: 6–35<br />
Math Applications<br />
Exercises 4 and 14 from<br />
pages 422–429<br />
START UP<br />
Tell students that convergence<br />
of an infinite series is the basis<br />
for the Fundamental Theorem<br />
of Calculus. Discuss with<br />
students the fact that while<br />
both arithmetic and geometric<br />
sequences can be infinite, only<br />
geometric series converge.<br />
INSTRUCTION<br />
Show students this infinite<br />
geometric series on a spreadsheet.<br />
In column A, generate 10 terms.<br />
In column B, generate 50 terms.<br />
In column C, generate 100 terms.<br />
Use the Sum Formula at the end<br />
of each column. Emphasize the<br />
convergence of the sums.<br />
a1<br />
Use the formula S =<br />
1− r<br />
to<br />
verify that the sum of this series<br />
diverges to 4 as shown in the<br />
spreadsheet.<br />
9.4 Infinite Geometric Series 409
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