Functions can often be represented by an infinite series. A series representation can help to solve...

   

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Functions can often be represented by an infinite series. A series representation can help to solve differential equations, to find derivatives, or to compute integrals involving the function. Computers also use these series representations to perform calculations. For example, 0³ 05 + 3! 5! allows a calculator to give a decimal approximation of values of sine. sin (0) = 0 - 07 7! + ... road 0= angle sin(0)=0- 0³ 05 + 3! - 07 +... Select Scenario 1, the series (-1). This series converges by the Alternating Series Test. (a) According to the alternating series estimate, what is the minimum value of n needed to approximate S, within 42 24 n=25 x (b) Give the partial sum 5, for the value of n from part (a). (Round to two places after the decimal.) x S-0.67 Functions can often be represented by an infinite series. A series representation can help to solve differential equations, to find derivatives, or to compute integrals involving the function. Computers also use these series representations to perform calculations. For example, 0³ 05 + 3! 5! allows a calculator to give a decimal approximation of values of sine. sin (0) = 0 - 07 7! + ... road 0= angle sin(0)=0- 0³ 05 + 3! - 07 +... Select Scenario 1, the series (-1). This series converges by the Alternating Series Test. (a) According to the alternating series estimate, what is the minimum value of n needed to approximate S, within 42 24 n=25 x (b) Give the partial sum 5, for the value of n from part (a). (Round to two places after the decimal.) x S-0.67

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