Final answer:
The expression Σₗ=5ⁿ (3j²) is correctly rewritten using summation formulas as (3Σₗ=5ⁿj²), which factors out the constant 3 from the summation over j².
Step-by-step explanation:
The goal is to rewrite the sum Σₗ=5ⁿ (3j²) using summation formulas. The correct reformulation using summation notation is option (a), which represents the sum of the squares of each term multiplied by 3, that is, (3Σₗ=5ⁿj²).
To see why, let's consider that multiplying each term in the summation by a constant simply factors that constant out of the summation. So if our terms inside the summation are 3j², we can take out the constant 3 and leave the summation over j², which is exactly what option (a) shows.
The other options either manipulate the summation incorrectly or represent a different mathematical expression. For example, option (b) squares the entire term 3j, option (c) is a multiplication of two different summations, which is not equivalent to the original expression, and option (d) is the same mistake as option (b).