Thread: Induction Problem

Prove the following statement:

(For all natural numbers n)(Summation from k=1 to n (1/k>=ln(n+1))
Some induction books use P(0) as the base case, in my book we use P(1), anybody kno how to approach?

Also we may use the fact that ln(1+x)<= x whenever x belongs to real numbers and x >=0

Originally Posted by ruprotein

Prove the following statement:

(For all natural numbers n)(Summation from k=1 to n (1/k>=ln(n+1))
Some induction books use P(0) as the base case, in my book we use P(1), anybody kno how to approach?

Also we may use the fact that ln(1+x)<= x whenever x belongs to real numbers and x >=0

Lets assume that the base case P(1) has been demonstrated.

Suppose P(n) is true,m then:



so:



Now:

,

so:




which is what we need to complete the proof.

RonL