Write the Word or Phrase That Best Completes Each Statement $$2 + 4 + 6 + 8 + \cdots + 2 n = n ^ { 2 } + n + 3$$

Essay

Write the word or phrase that best completes each statement or answers the question.
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
-Show that the formula
$$2 + 4 + 6 + 8 + \cdots + 2 n = n ^ { 2 } + n + 3$$
obeys Condition II of the Principle of Mathematical Induction. That is, show that if the formula is true for some n number $k _ { t }$ it is also true for the next natural number $k + 1$ . Then show that the formula is false for $n = 1$ . atural