Rational Numbers, Decimals, Geometric Series, Approximations Page 2
ADVERTISEMENT
1
29. Determine the sum of the following geometric series or explain why the formulas above are not
applicable. You do not need to simplify your answers.
(a) 1024 + 512 + 256 + 128 +
+ 4 + 2 + 1
2
4
6
16
(b) 1 + 5
+ 5
+ 5
+
+ 5
1
1
1
(c) 1 +
+
+
+
3
9
27
(d) 5 + 10 + 20 + 40 +
4
8
(e) 3 + 2 +
+
+
3
9
2
4
6
2
2
2
(f)
+
+
+
2
3
3
3
3
1
1
(g) 8
4 + 2
1 +
+
2
4
(h) 1 + 0.4 + 0.16 + 0.064 +
(i) 0.6 + 0.18 + 0.054 +
10. Rewrite the following repeating decimals as infinite series. Compute their sums and write your
answer as a simplified fraction.
(a) 0.4 = 0.44444 . . .
(b) 0.7 = 0.77777 . . .
(c) 0.13 = 0.13131313 . . .
(d) 0.05 = 0.05050505 . . .
(e) 0.21 = 0.21111111 . . .
(f) 0.015 = 0.0151515 . . .
11. A rubber ball rebounds to two thirds of the height from which it falls. If it is dropped from a
height of 4 feet and is allowed to continue bouncing forever, what is the total distance it travels?
12. Approximate the following quantities without using a calculator.
(a) 3.2406
100.012
(b) 56.43
0.00103
(c) 0.124
161
(d) 13.813 + 840.199
(e) 8
0.249
2
3
(f) 4.002
2.013
4.997
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education