College Algebra, 2013a

670 Sequences and the Binomial Theorem
9.2.1 Exercises
In Exercises 1 - 8, find the value of each sum using Definition 9.3.
1.
9∑
(5g +3) 2.
g=4
8∑
k=3
1
k
3.
5∑
2 j 4.
j=0
2∑
(3k − 5)x k
k=0
5.
4∑
i=1
1
4 (i2 +1) 6.
∑100
(−1) n 7.
n=1
5∑
n=1
(n +1)!
n!
8.
3∑
j=1
5!
j!(5− j)!
In Exercises 9 - 16, rewrite the sum using summation notation.
9. 8 + 11 + 14 + 17 + 20 10. 1 − 2+3− 4+5− 6+7− 8
11. x − x3
3 + x5
5 − x7
7
12. 1+2+4+···+2 29
13. 2 + 3 2 + 4 3 + 5 4 + 6 5
14. − ln(3) + ln(4) − ln(5) + ···+ ln(20)
15. 1 − 1 4 + 1 9 − 1
16 + 1
25 − 1
1
36
16.
2 (x − 5) + 1 4 (x − 5)2 + 1 6 (x − 5)3 + 1 8
(x − 5)4
In Exercises 17 - 28, use the formulas in Equation 9.2 to find the sum.
17.
∑10
n=1
5n + 3 18.
∑20
n=1
2n − 1 19.
∑15
k=0
3 − k
20.
∑10
n=1
( 1
2
) n
21.
5∑
( ) 3 n
22.
2
n=1
5∑
k=0
( 1 k
2
4)
23. 1+4+7+...+ 295 24. 4 + 2 + 0 − 2 − ...− 146 25. 1 + 3 + 9 + ...+ 2187
26.
1
2 + 1 4 + 1 8 + ...+ 1
256
27. 3 − 3 2 + 3 4 − 3 8 + −···+ 3
256
28.
∑10
n=1
( 5 n
−2n +
3)
In Exercises 29 - 32, use Theorem 9.2 to express each repeating decimal as a fraction of integers.
29. 0.7 30. 0.13 31. 10.159 32. −5.867