Q6 Please help me answer all parts to this practice calculus question The Cauchy condensation test says the following. "Let (a, be a nonincreasing sequence (an z an +1 for all n) of positive terms that converges to 0.%3D2n1 diverges. Show why the test works.State the Cauchy condensation test symbolically. Choose the correct answer below.0000O A. 2 an = 0 +E 2"a,n = 0n=1-n = 100O B. 2 an =0 + 2 2"a,n < 00n= 1n= 10000O C. 2 an < 00 +E 2"a,n < 00n=1n= 10000Assume an < 0o. Show that 2 2"a,n< 00, List the first few terms of the seriesan < 0o. Choose the correct answer below.n= 1n= 1n= 1+ (an + an + an + an) + (an+ an + .. + an... < 00O A. an + an + (an + anO B. a, +a2 + (a3 + a4) + (a5 + a6 + a7 + ag) + (ag + a10 Rewrite the terms using the fact that a, zan11 for all n. Choose the correct answer below.- 1O A. an+1*an+1* (an+1+an+1) + (an+1 + an+1 + an + an)+ .. < 00O B. a1 -a2- (a4 +a4) - (ag +ag -ag + ag) - (a16 + a16 + …*+a16) -- ... < 00Oc. a1 +a, + (a4 + a4) + (ag + ag + ag + ag) + (a16 + a16a16) *+ ... ++ ... < 00Multiply each term in the şeries by 2.O A. 2an+1+2an+1* (2an + 1+ 2an+1) + (2an + 1 + 2an +1+ 2an + 2an) + ... < co2a16)B. 2a1 - 2a2 - (2a4 + 2a4) - (2ag + 2ag - 2ag + 2ag)- (2a16 + 2a16 + - ++ ... < 0oOc. 2a, + 2a, + (2a1 + 2a1) + (2ag + 2ag + 2ag + 2ag) + (2a16 + 2a16+ .. + 2a16)...< 00What can be said about the series now?0000O A. The series equals 2a, + 2"a,n < o, so it follows that 2" a,n << 00

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Description: Q6 Please help me answer all parts to this practice calculus question The Cauchy condensation test says the following. "Let (a, be a nonincreasing sequence (an z an +1 for all n) of positive terms that converges to 0.%3D2n1 diverges. Show why the tes

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Q6 Please help me answer all parts to this practice calculus que

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.2: Exponents And Radicals

Problem 90E

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Q6 Please help me answer all parts to this practice calculus question

The Cauchy condensation test says the following. "Let (a, be a nonincreasing sequence (an z an +1 for all n) of positive terms that converges to 0.
%3D
2n
1 diverges. Show why the test works.
State the Cauchy condensation test symbolically. Choose the correct answer below.
00
00
O A. 2 an = 0 +
E 2"a,n = 0
n=1
-n = 1
00
O B. 2 an =0 + 2 2"a,n < 00
n= 1
n= 1
00
00
O C. 2 an < 00 +
E 2"a,n < 00
n=1
n= 1
00
00
Assume an < 0o. Show that 2 2"a,n
< 00, List the first few terms of the series
an < 0o. Choose the correct answer below.
n= 1
n= 1
n= 1
+ (an + an + an + an) + (an
+ an + .. + an
... < 00
O A. an + an + (an + an
O B. a, +a2 + (a3 + a4) + (a5 + a6 + a7 + ag) + (ag + a10

Rewrite the terms using the fact that a, zan11 for all n. Choose the correct answer below.
- 1
O A. an+1*an+1* (an+1+an+1) + (an+1 + an+1 + an + an)
+ .. < 00
O B. a1 -a2- (a4 +a4) - (ag +ag -ag + ag) - (a16 + a16 + …*+
a16) -
- ... < 00
Oc. a1 +a, + (a4 + a4) + (ag + ag + ag + ag) + (a16 + a16
a16) *
+ ... +
+ ... < 00
Multiply each term in the şeries by 2.
O A. 2an+1+2an+1* (2an + 1
+ 2an+1) + (2an + 1 + 2an +1+ 2an + 2an) + ... < co
2a16)
B. 2a1 - 2a2 - (2a4 + 2a4) - (2ag + 2ag - 2ag + 2ag)- (2a16 + 2a16 + - +
+ ... < 0o
Oc. 2a, + 2a, + (2a1 + 2a1) + (2ag + 2ag + 2ag + 2ag) + (2a16 + 2a16
+ .. + 2a16)
...< 00
What can be said about the series now?
00
00
O A. The series equals 2a, + 2"a,n < o, so it follows that 2" a,n <
< 00

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