- #1

srfriggen

- 306

- 5

## Homework Statement

Ʃ 1/√k ≥ 1/√n (under sigma should be "k=1" and above should be "n", and n is a positive integer)

## Homework Equations

## The Attempt at a Solution

I. Base case when n=1 is correct.

II. Inductive Hypothesis: Assume true for k=m, where k<m<n, m is a positive integer.

III. Ʃ 1/√m + 1/√m+1 ≥ 1/√n, since Ʃ 1/√m ≥ 1/√n, and Ʃ 1/√m + 1/√m+1 ≥ Ʃ 1/√m.

By the principle of induction, Ʃ 1/√k ≥ 1/√n.

(I'm sorry for leaving out some subscripts under epsilon. I couldn't find how to get k=1 under there or "n" above).