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... :/ )