MediumDerivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §1.2 Calculus Without Limits, #28 · Calculus · Derivatives

Suppose the …'s increase by 4 at every step

This problem involves numbers $f_{0}, f_{1}, f_{2}, \dots$ and their differences $v_{j} = f_{j} - f_{j - 1}$ . They give practice with subscripts $0, \dots, j$ .

Suppose the $v$ 's increase by 4 at every step. Show by example and then by algebra that the "second difference" $f_{j + 1} - 2 f_{j} + f_{j - 1}$ equals 4.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §1.2 Calculus Without Limits, #28

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