Final answer:
The Riemann sum formula is written as Σ f(xi)Δx and is used to approximate definite integrals. The moment of inertia for a system of point particles is calculated with the formula I = Σmiri². Ohm's law for parallel resistances also utilizes a summation expression.
Step-by-step explanation:
The formula for a Riemann sum is used in calculus to approximate the area under a curve. This is usually written as Σ f(xi)Δx, where f(xi) is the function being integrated, xi is the ith value of x, and Δx is the width of each subdivision or 'slice' of the domain. The limit of the Riemann sum as Δx approaches zero gives us the definite integral of the function.
To calculate the moment of inertia I for a system of point particles, one would use the summation formula I = Σmiri2. In this formula, mi represents the mass of each particle and ri represents the distance from each particle to the axis of rotation.
Additionally, complex relationships such as Ohm's law for parallel resistances can be expressed using a summation formula like 1 / Requiv = Σ(1 / Ri), where Requiv is the equivalent resistance.