. Starting with the generating function for 1,2, 3, 4, ..., find a generating function for each of the following sequences. а. 1,0, 2,0, 3, 0, 4,.... b. 1, -2,3, –4, 5, –6, .. с. 0, 3, 6, 9, 12, 15, 18, ... d. 0,3,9, 18, 30, 45, 63, .... (Hint: relate this sequence to the previous one.) Solution a. (1-1*)* b. ui (1+2)a C. (1–z)* ' d. (1-z) (partial sums).

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A: I have provided solution in step 2.

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Q: thanks for the help but could you solve for d as well as I asked?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.