Suppose a is a real number and 1 + a > 0. Prove that (1 +...

Question

Question

Answer 1

Answer #1

let, a is a real number and taso To prove (Ita) nitha una we shall prove this using malhomatical induction. Firstly show for

Answer 2

Similar Homework Help Questions

a be a real number . If a--a, prove that either a 0 or a 1....

a be a real number . If a--a, prove that either a 0 or a 1. 8. (Pigeonhole Principle) Suppose we place m pigeons in n pigeonholes, where m and n are positive integers. If m > n, show that at least two pigeons must be placed in the same pigeonhole. [Hint (from Robert Lindahl of Morehead State University): For i 1, 2, . . . , n, let Xi denote the number of pigeons that are placed in the...
Prove that for all integers n > 0, 2 (na + n).

Prove that for all integers n > 0, 2 (na + n).
17. Suppose that limn70 An = L. a.) Prove that if an > 0 for all...

17. Suppose that limn70 An = L. a.) Prove that if an > 0 for all ne N, then L > 0. b.) Give an example to show that an > 0 for all n E N does not imply that L >0.

induction question, thanks. (15 points) Prove by induction that for an odd k > 1, the...

induction question, thanks. (15 points) Prove by induction that for an odd k > 1, the number 2n+2 divides k2" – 1 for all every positive integer n.
8. Prove that max { x ( 2 -*): x is a real number} < 1...

8. Prove that max { x ( 2 -*): x is a real number} < 1 using the MAX/MIN method. 9 Sunoco thot Sand Taro qubooto ful
14. Use L'Hospital's rule to prove that a" = win"), for every real a > 1...

14. Use L'Hospital's rule to prove that a" = win"), for every real a > 1 and integer k > 1.

Prove that for every positive real (important: is not necessarily an integer), that . Hint: For...

Prove that for every positive real (important: is not necessarily an integer), that . Hint: For every , the function is strictly growing. We were unable to transcribe this imageWe were unable to transcribe this imagebe(n") (n log, n) > 0 n
real analysis. questions Prove that if lima In = 0 and > M for some M...

real analysis. questions Prove that if lima In = 0 and > M for some M >0 and in 10 > 0, then lima (ny) - Asume 30 = 2,2-20+ In+1 = In + Prove that this sequence has a limit and find the limit. Prove that lim = L with L < if and only if every subsequence limo n L. Suppose that the sequence {an) is increasing and the sequence {yn) is decreasing. Moreover, lim a n -...
use all 3 cases please 0. Prove that for every real number x, if -3| >...

use all 3 cases please 0. Prove that for every real number x, if -3| > 3 then x2 > 6x. Proof: Given |x - 3]> 3.

real analysis hint 13 Suppose fis a continuous function on R', with period 1. Prove that...

real analysis hint 13 Suppose fis a continuous function on R', with period 1. Prove that lim Σ f(a)-| f(t) dt 0 for every irrational real number α. Hint: Do it first for f(t)= exp (2nikt), k = 0,±1, ±2, 4.13 Let 2 be the set of functions of form P(t)-Σ_NQC2nikt. The equality holds for functions in . For given ε > 0, there is a P E 2 such that llf-Plloo < ε. Then