First of all, please my poor English (I'm currently a French student trying to master mathematical redaction in another language... And I do find it difficult.)
So, I have an exercise I don't know how to handle...
Let (Wn) be a sequence such as W_n= sum from (k=1 to n) of (1/(n+k)^1/2). Prove that for any integer n, (n/2)^1/2<= (Wn)
I tried to prove it using induction:
Let for any positive integer be Pn:" (n/2)^1/2<=(Wn)
Basis: for n= 1, we have W_0= 1/(1+1)^1/2=1/(2)^1/2 , thus (P_0) is confirmed
Then I assumed Pn, and tried to study W(n+1)
Which I'm currently failing at...
Any tips, any idea about how I could resolve this?
Thanks for reading me! (And sorry for not using LaTEX, I'm currently trying to get accustomed to it... :/ )