**Unformatted text preview: **Math 21C
Kouba
Discussion Sheet 8 1.) Determine convergence 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. ' 00
2 3
a.) 3n + 2 (Use the nth term test.)
71:3 71+
0° ,_2 n+1
b.) 2 7(—3—n)_—1— (Use the geometric series test.)
n=4
°° 1
c. —— Use the —series test.
) 1;; nﬁ ( p )
0° 71
d.) 2 2 (Use the integral test.)
”:2 n + 4
°° 1 1
e. — ~ Use the se uence of artial sums test.
) ”2:; {m n + 2} ( q p - )
f ) i0: 11:: (Use the com arison test )
”:2 n3 + 2 p .
00 n3 + 7712 — 3 .
g ) Z —4 4 9 (Use the limit comparison test.)
n — n 2.) Use any test to determine the convergence or divergence of each series. 00 00 00 1 00
a.) Zeos(1/n2) b.) ZsinO/nZ) c.) Zn(lnn)2 d.) :3<2‘”) .
n21 n21 n=2 11:1
. 2 "3 . n . h. m
e); (n ) f)nZ:;)Vn3—i—8 “Elm—2n );1+2+3+-~+n
0° 1 ‘ 0° Inn
1) E E; J ) Z —3
71:3 71:2
3 ) Consider the series i 1
' ”:3 4n2 — 1 ‘ a.) Use the limit comparison test to show that the series converges. b.) Use partial fractions then the sequence of partial sums to ﬁnd the exact value of
this series. 4.) Find the exact value of the following convergent series : 3-3 3—1+31 33+35 37
101 102 103 104 105 106 5.) Use a geometric series to convert the decimal number 02525252525... to a fraction. “Talking is not teaching and listening is not learning.” — Unknown ...

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