A.) If {a,} is a convergent sequence, then {a,} is also a convergent sequence. B.) If f(x) is a positive decreasing continuous function defined for all x21 and if | f(x)dr converges, vo n booibni ort adr bnit then Ef(k) converges and Ef(k)<" f(x)dx k=1 k=2 0001 (b) F(0) C.) Suppose a, converges and b, converges with a, 20 and b, 20 for every i, then n=1 n=1 Σ(α-b) converges, n=1 D.) If b, is convergent, and 00 and lim a, <1, then lim a, = 0. Sogrovn n-00

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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I’m stuck on these true or false hw questions. Thank you
A.) If {a,} is a convergent sequence, then {a,} is also a convergent sequence.
(1)
B.) If f(x) is a positive decreasing continuous function defined for all x21 and if f(x)dx converges,
VO n boibni ort ot cmue dr bnin or robro
then Ef(k) converges and Ef(k)<f(x)dx
k=1
k=2
to ano
0001 (b)
a d)
C.) Suppose a, converges and b, converges with a, 20 and b, 20 for every i, then
n=1
n=1
E(a, -b,) converges
J2same orlt at tadw rods E-x molw 2ogoveo (S-x) or eo
n=1
00
D.) If b, is convergent, and 0<a, sb, for all k then a, is convergent
k=1
k=1
oelo 120n iwollo
E.) If a, >0 and lim la, <1, then lim a, = 0.
foyrovno
n-→の
Transcribed Image Text:A.) If {a,} is a convergent sequence, then {a,} is also a convergent sequence. (1) B.) If f(x) is a positive decreasing continuous function defined for all x21 and if f(x)dx converges, VO n boibni ort ot cmue dr bnin or robro then Ef(k) converges and Ef(k)<f(x)dx k=1 k=2 to ano 0001 (b) a d) C.) Suppose a, converges and b, converges with a, 20 and b, 20 for every i, then n=1 n=1 E(a, -b,) converges J2same orlt at tadw rods E-x molw 2ogoveo (S-x) or eo n=1 00 D.) If b, is convergent, and 0<a, sb, for all k then a, is convergent k=1 k=1 oelo 120n iwollo E.) If a, >0 and lim la, <1, then lim a, = 0. foyrovno n-→の
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