The equation in the image provided is:

$2 + 6 + 12 + \dots + n(n+1) = n(n+2), \quad n \geq 1.$

This represents a sum of multiples, likely based on an arithmetic or quadratic pattern.

To clarify:

• The left-hand side seems to be the sum of terms, where the general form for the $k$-th term appears to be $k(k+1)$, which begins with $2(2+1) = 6$, followed by $3(3+1) = 12$, and so on until $n(n+1)$.

The right-hand side is $n(n+2)$, which simplifies to a quadratic expression.

Let's confirm and analyze the relationship:

1. Sum pattern: The left-hand side is a sum of terms of the form $2 + 6 + 12 + \cdots + n(n+1)$.
2. Target identity: It is to be shown that this sum equals the quadratic expression $n(n+2)$.

Would you like me to go through the detailed steps to prove this identity?