MediumDerivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §1.2 Calculus Without Limits, #23 · Calculus · Derivatives

If … then

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 $0, \dots, j$ .

If $v = 1, 3, 5, \dots$ then $f_{j} = j^{2}$ . If $v = 1, 1, 1, \dots$ then $f_{j} =____$ . Add those to find the sum of $2, 4, 6, \dots, 2 j$ . Divide by 2 to find the sum of $1, 2, 3, \dots, j$ . (Compare Problem 22.)

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §1.2 Calculus Without Limits, #23

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