12 1 pt determine the sum of the following series n 1

• 4*(1 - 0.5ˆ(14+1))/(1 - 0.5)
• (13-5+1)
• 4*(0.5ˆ(5))(1 - 0.5ˆ(13-5+1))/(1 - 0.5)
14. (1 pt) Express 8 . 684684684 ... as a rational number, in
the form
p
q
where p and q have no common factors.
p = and
q =
Correct Answers:
• 964
• 111
15. (1 pt) Find the first five partial sums of the following se-
ries. Then find the sum if it is convergent. If it is divergent, type
”Diverges” or ”D”.
n ( n + 2 )
∞
∑
n = 1
( - 3 )
n - 1
7
n
1/4-1/(4+2)
• 1/4-1/(4+2)+1/(4+1)-1/(4+3)
• 1/4+1/(4+1)-1/(4+3)-1/(4+4)
• 1/4+1/(4+1)-1/(4+4)-1/(4+5)
• 1/4+1/(4+1)-1/(4+5)-1/(4+6)
13. (1 pt) For each of the finite geometric series given below,
indicate the number of terms in the sum and find the sum. For
• 1/4-1/(4+2)
• 1/4-1/(4+2)+1/(4+1)-1/(4+3)
• 1/4+1/(4+1)-1/(4+3)-1/(4+4)
• 1/4+1/(4+1)-1/(4+4)-1/(4+5)
• 1/4+1/(4+1)-1/(4+5)-1/(4+6)
the value of the sum, enter an expression that gives the exact
value, rather than entering an approximation.
A. 4 + 4 ( 0 . 5 )+ 4 ( 0 . 5 )
2
+ ··· + 4 ( 0 . 5 )
14
number of terms =
value of sum =
B. 4 ( 0 . 5 )
5
+ 4 ( 0 . 5 )
6
+ 4 ( 0 . 5 )
7
+ ··· + 4 ( 0 . 5 )
13
number of terms =
value of sum =
∞
∑
k = 2
3
( k - 1 ) 2
-
3
k 2
a) Determine whether the series is convergent or divergent:
.
(Enter ”convergent” or ”divergent” as appropriate.)
b) If it converges, find its sum: .
If the series diverges, enter here ”divergent” again.
3
12. (1 pt) Determine the sum of the following series.
s
4
= , s
5
= , s
6
= , s
7
= , and s
8
=