(1) Find the first five partial sums of the given series and determine whether t
ID: 2845986 • Letter: #
Question
(1) Find the first five partial sums of the given series and determine whether the series appears to be convergent or divergent. If it is convergent, find its approximate sum.
1/8 - 1/64 + 1/512 - 1/4096 + 1/32768 - ....
S1=
S2 =
S3 =
S4 =
S5 =
Does this series appears to converge or diverge? If it converges, what is its approximate sum?
Choose the correct answer below and , if necessary, fill in the answer box to complete your choice.
(1) The series appears to converge to ........... (Round to two decimal places as needed)
(2) The series appears to diverge.
Explanation / Answer
S1= 1/8 = 0.125
S2 = 7/64 = 0.109375
S3 = 57/512 = 0.11328
S4 = 455/4096 = 0.11108
S5 = 3641 / 32768 = 0.11111
given series is Geometric progression with common ratio = r = -1/8
since |r| < 1 so theries is converging
Sum = a/(1-r) = (1/8) / (1-(-1/8)) = 1/9 = 0.111111
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