Prove by induction the following inequality for all n N Sol

Prove by induction the following inequality for all n N :

Solution

suppose the given equation is correct

let n = k+1

1/(sqrt1) + 1/(sqr2)+....+1/sqrt(k)+1/(sqrtK+1))

<=sqrt(k)+1/(sqrt(k+1)

<=(sqrt(k*(k+1))+1)/(sqrtk+1)

<= sqrt(k+1)

hence proved by induction