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Prove inequality about sequences

  • #1

Homework Statement


Let [tex]u_n, v_n[/tex] be a sequence of positive real number such that
[tex]u_{n+1}\leq (1+v_n)u_n[/tex] where [tex]\sum_{n=1}^{\infty}v_n[/tex]
converges.

It is true or false if true please help me prove.
if [tex]\frac{u_{n+1}}{u_n}\leq M [/tex] then [tex]u_n\leq M[/tex]
for some [tex]M[/tex] be a positive real number.

whether we can find [tex]M[/tex] is a positive real number such that
[tex]u_n\leq M[/tex] for all natural number n


Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

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