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**Unformatted text preview: **Math 210
Kouba
Discussion Sheet 9 1.) Determine conVrergence or divergence of each series using the test indicated. I suggest
that you read all of the assumptions and conclusions for each test from the handout I gave
last time as you do% each problem‘ n~1 n3
0; 7
c ) Z(—1)"+1 2 3 (Use the alternating series test.)
n
n=1
1 ‘1 1 l 1 1 l 1
d.) 1+ — — ~— + — + —— — — + — + — — —— + (Use the absolute conver— e.) Z(—1)"(l/10) (Use the sequence of partial sums test.) 11.20 00 f.) 2 (Use the limit comparison test.)
n=1 2.) Use a geometric series to convert the decimal number 0.777777777... to a fraction. 00
1
3. The series — diver es.
) n; n g
a.) Use equation to determine between which two numbers the partial sum
50 1
S50 2 Z lies. i=1 n 1
b.) What should n be in order that the partial sum 5' : Z —. be at least 20 ?
1 i=1 ” 1
C.) What is the largest value of n for which the partial sum Sn 2 Z does not i=1 exceed 50 ?
Tl ' 00 4.) 1e series E converges.
_ ‘ 5 1
a.) Compute the partial sum S5 = E 3. Use to estimate the resulting error.
7, i=1 17. 1
b.) What should n be in order that the partial sum 5' = Z 3 estimate the exact
2
i=1
value of the series with error at most 0.0001 ? 00
1
5.) The alternating; series Z(~1)"+17—13 converges.
n=1 5
. 1 .
a.) Compute the partial sum 5'5 : E (—1)‘+1,—3—. Estimate the resulting absolute
2
i=1 error. Between what two numbers does the exact value of the series lie ? n . 1
b.) What should 7?. be in order that the partial sum Sn : :(—1)’+1i—3 estimate the
i=1 exact value of the series with absolute error at most 0.0001 ? “What is important is to keep learning, to enjoy challenge, and to tolerate ambiguity. In
the end there are no certain answers.” — Martina Horner ...

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