(1) Find the first five partial sums of the given series and determine whether t
ID: 2832257 • 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+ 1/4 + 1/9 + 1/16 + 1/25 + ....
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
1+ 1/4 + 1/9 + 1/16 + 1/25
S1 = 1
S2 = 1.25
S3 = 1+ 1/4 + 1/9 = 1.361
S4 = 1+ 1/4 + 1/9 + 1/16 = 1.424
S5 = 1+ 1/4 + 1/9 + 1/16 + 1/25 = 1.463
It converges
Approximate sum = sigma( 1/n^2) = pi^2/6 = 1.6449
Answer : The series appears to converge to 1.64
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