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The integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the integral J F(x)dx is convergent as long as the function f is BLANK-1, BLANK- 2, and BLANK-3 on the interval X21. BLANK-1 Add your answer BLANK-2 Add your answer BLANK-3 Add your answer .T dx= lim x-2dx= lim -Tl+1¬1= lim +1 = 1 Since the integral converges and therefore the series 2 K=1 K? also converges, and <1+1=2. K=1 K2

The integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the integral J F(x)dx is convergent as long as the function f is BLANK-1, BLANK- 2, and BLANK-3 on the interval X21. BLANK-1 Add your answer BLANK-2 Add your answer BLANK-3 Add your answer .T dx= lim x-2dx= lim -Tl+1¬1= lim +1 = 1 Since the integral converges and therefore the series 2 K=1 K? also converges, and <1+1=2. K=1 K2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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The integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the integral J F(x)dx is convergent as long as the function f is BLANK-1, BLANK- 2, and BLANK-3 on the interval X21. BLANK-1 Add your answer BLANK-2 Add your answer BLANK-3 Add your answer .T dx= lim x-2dx= lim -Tl+1¬1= lim +1 = 1 Since the integral converges and therefore the series 2 K=1 K? also converges, and <1+1=2. K=1 K2
Transcribed Image Text:The integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the integral J F(x)dx is convergent as long as the function f is BLANK-1, BLANK- 2, and BLANK-3 on the interval X21. BLANK-1 Add your answer BLANK-2 Add your answer BLANK-3 Add your answer .T dx= lim x-2dx= lim -Tl+1¬1= lim +1 = 1 Since the integral converges and therefore the series 2 K=1 K? also converges, and <1+1=2. K=1 K2
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for integral test three conditions must be satisfied for the function i.e.  continuous, positive and decreasing.

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