What would you like to understand?

Assume $P(k)$ is true: $2 + 4$ + ... + $2k = k(k+1)$. To prove $P(k+1)$, write the LHS as the sum up to 2k plus the next term $2(k+1)$.

Conditions: Inductive hypothesis: $P(k)$ is true.; Goal: Prove $P(k+1)$ is true.; Algebraic manipulation involves factoring common terms.

Assume $P(k)$ is true: $2 + 4$ + ... + $2k = k(k+1)$. To prove $P(k+1)$, write the LHS as the sum up to 2k plus the next term $2(k+1)$.

Conditions: Inductive hypothesis: $P(k)$ is true.; Goal: Prove $P(k+1)$ is true.; Algebraic manipulation involves factoring common terms.