Now prove the required result. For n=1 (1+x} 21+x[As 1+x=1+x] Let us assume the result for n=k |(1+x)* >1+kx ...(4) Now prove the result for n = k+1 k+1 To prove: (1+x)** >1+(k+1)x Consider: (1+x)* = (1+ x)* (1+x) 2(1+ kx)(1+x)[From (4)] k+1 %3D 21+x+kx+ kx² 21+(1+x)k+ kx² |(1+x)* >1+(1+x)k| k+1
Now prove the required result. For n=1 (1+x} 21+x[As 1+x=1+x] Let us assume the result for n=k |(1+x)* >1+kx ...(4) Now prove the result for n = k+1 k+1 To prove: (1+x)** >1+(k+1)x Consider: (1+x)* = (1+ x)* (1+x) 2(1+ kx)(1+x)[From (4)] k+1 %3D 21+x+kx+ kx² 21+(1+x)k+ kx² |(1+x)* >1+(1+x)k| k+1
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Now prove the required result.
For n=1
(1+x)' 21+x[As 1+x=1+x]
Let us assume the result for n= k
(1+x)* >1+kx.(4)
Now prove the result for n =k+1
To prove: (1+x)*>1+(k+1)x
Consider:
(1+x}* = (1+x)*(1+x)
2(1+kx)(1+x)[From (4)]
k+1
21+x+kx+kx?
21+(1+x)k+kx²
|(1+x)** >1+ (1+x)k](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F06a2994e-9ea9-4c4e-b01c-652fae7627ae%2F0a093aaa-59c2-421f-abc9-577ca846198a%2Fz9mo7mh_processed.png&w=3840&q=75)
Transcribed Image Text:Now prove the required result.
For n=1
(1+x)' 21+x[As 1+x=1+x]
Let us assume the result for n= k
(1+x)* >1+kx.(4)
Now prove the result for n =k+1
To prove: (1+x)*>1+(k+1)x
Consider:
(1+x}* = (1+x)*(1+x)
2(1+kx)(1+x)[From (4)]
k+1
21+x+kx+kx?
21+(1+x)k+kx²
|(1+x)** >1+ (1+x)k
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