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Prove each of the statements in 10-18 by mathematical induction 12. 1/(1*2)+1/(2*3)+. . . + 1/(n(n+1))=n/(n+1), for every integer n> =1 P(1) 1/(1(1+1) = 1/2 P(1) is not true P(2) 1/(2(2+1)) =1/6 +1/2 =2/3 =2/(2+1) P(2) is true P(k) = 1/(1*2)+1/(2*3)+. . . + 1/(k(k+1))=k/(k+1) P(k+1) = 1/(1*2)+1/(2*3)+. . . + 1/(k+1(k+2))=k+1/(k+2)

Prove each of the statements in 10-18 by mathematical induction 12. 1/(1*2)+1/(2*3)+. . . + 1/(n(n+1))=n/(n+1), for every integer n> =1 P(1) 1/(1(1+1) = 1/2 P(1) is not true P(2) 1/(2(2+1)) =1/6 +1/2 =2/3 =2/(2+1) P(2) is true P(k) = 1/(1*2)+1/(2*3)+. . . + 1/(k(k+1))=k/(k+1) P(k+1) = 1/(1*2)+1/(2*3)+. . . + 1/(k+1(k+2))=k+1/(k+2)

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 30E: 30. Prove statement of Theorem : for all integers .
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Prove each of the statements in 10-18 by mathematical induction

12.

1/(1*2)+1/(2*3)+. . . + 1/(n(n+1))=n/(n+1), for every integer n> =1

P(1)

1/(1(1+1) = 1/2

P(1) is not true

P(2)

1/(2(2+1)) =1/6 +1/2 =2/3 =2/(2+1)

P(2) is true

P(k) = 1/(1*2)+1/(2*3)+. . . + 1/(k(k+1))=k/(k+1)

P(k+1) = 1/(1*2)+1/(2*3)+. . . + 1/(k+1(k+2))=k+1/(k+2)

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