# TADM2E 1.17

From Algorithm Wiki

**Step 1:** Show that the statement holds for the basis case $ n = 1 $

- $ E(n) = n - 1 $

- $ E(1) = 1 - 1 = 0 $. A tree with one node has zero edges

**Step 2:** Assume that that summation is true up to *n*.

**Step 3:** Show that on the assumption that the summation is true for *n*, it follows that it is true for *n + 1*.

- $ E\left(n + 1\right) = n + 1 - 1 $

- $ \Leftrightarrow E(n) + 1 = n $ When adding one node to a tree one edge is added as well

- $ \Leftrightarrow n -1 + 1 = n $

- $ \Leftrightarrow n = n $

QED