910 Each of the following series is convergent. Find their sums. (a) n=2 (b) n=1 3 n²+7n+12 n=2 (5)" 4 (33) = 4 (())" = 4 (3)" 41号)=4(言 4(号) Geometric series Irl ====<| converges है n=2 ༢ 2 -(s) = 4 (2-1)) = 4 (4-5) = 4 (1/3) -1 =2 4 12++黒点 4(+) = 4 (1) --6 12+ (-6)+(-6)=0 3 b n=1 3 52+75+12 टै 3 3 B n=1 (n+3)(n+4) + (n+3)(n+4) 1+3 n+4. 3= A(n+4)+B (n+b) L>Let n=-4 3=B(-1) 3-B ↳ Let x=-3 3=A(-3+4) n= S= h+3 3 लग 4 - 一 3 n+4 5 52 = ( 2/4 - 2) + 15 512 20 3 = A 층) 5% -동) 12 20 له 2 लात 53 = ( 4 − 3 ) + ( ²² - 3) + (z - 3/3) 54 = ( ²² - } } ) + ( } } } ) + ( − 2 ) + ( 3 3 3 ) 3 3 SK = 4 TK+2 So this series converges to 30 20
910 Each of the following series is convergent. Find their sums. (a) n=2 (b) n=1 3 n²+7n+12 n=2 (5)" 4 (33) = 4 (())" = 4 (3)" 41号)=4(言 4(号) Geometric series Irl ====<| converges है n=2 ༢ 2 -(s) = 4 (2-1)) = 4 (4-5) = 4 (1/3) -1 =2 4 12++黒点 4(+) = 4 (1) --6 12+ (-6)+(-6)=0 3 b n=1 3 52+75+12 टै 3 3 B n=1 (n+3)(n+4) + (n+3)(n+4) 1+3 n+4. 3= A(n+4)+B (n+b) L>Let n=-4 3=B(-1) 3-B ↳ Let x=-3 3=A(-3+4) n= S= h+3 3 लग 4 - 一 3 n+4 5 52 = ( 2/4 - 2) + 15 512 20 3 = A 층) 5% -동) 12 20 له 2 लात 53 = ( 4 − 3 ) + ( ²² - 3) + (z - 3/3) 54 = ( ²² - } } ) + ( } } } ) + ( − 2 ) + ( 3 3 3 ) 3 3 SK = 4 TK+2 So this series converges to 30 20
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:910
Each of the following series is convergent. Find their sums.
(a)
n=2
(b)
n=1
3
n²+7n+12
n=2
(5)"
4 (33) = 4 (())" = 4 (3)"
41号)=4(言
4(号)
Geometric series Irl ====<| converges
है
n=2
༢
2 -(s) = 4 (2-1)) = 4 (4-5) = 4 (1/3) -1
=2
4
12++黒点
4(+) = 4 (1) --6
12+ (-6)+(-6)=0
3
b
n=1
3
52+75+12
टै
3
3
B
n=1 (n+3)(n+4)
+
(n+3)(n+4)
1+3
n+4.
3= A(n+4)+B (n+b)
L>Let n=-4
3=B(-1)
3-B
↳ Let x=-3
3=A(-3+4)
n=
S=
h+3
3
लग
4
-
一
3
n+4
5
52 = ( 2/4 - 2) +
15
512
20
3 = A
층)
5% -동)
12
20
له
2
लात
53 = ( 4 − 3 ) + ( ²² - 3) + (z - 3/3)
54 = ( ²² - } } ) + ( } } } ) + ( − 2 ) + ( 3 3 3 )
3
3
SK =
4
TK+2
So this series converges to 30
20
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