14. Show that ifr>0, then, for each natural number n, (1+r)" >1+n•r.

College Algebra
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ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
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Homework 1
BOOK : Real-Analysis-4th-Edition-by HL Royden
Page 13: questions : 14, 15.
14. Show that if r >0, then, for each natural number n, (1+r)" >1+n•r.
15. Use induction arguments to prove that for every natural number n,
(i)
n(n+1)(2n + 1)
6.
j=1
(i)
1+2° +...+n = (1+2+...+n)°.
(ii)
1--1
1+r+...+
if r 1
1-r
Transcribed Image Text:Homework 1 BOOK : Real-Analysis-4th-Edition-by HL Royden Page 13: questions : 14, 15. 14. Show that if r >0, then, for each natural number n, (1+r)" >1+n•r. 15. Use induction arguments to prove that for every natural number n, (i) n(n+1)(2n + 1) 6. j=1 (i) 1+2° +...+n = (1+2+...+n)°. (ii) 1--1 1+r+...+ if r 1 1-r
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