f8M9X_SequencesAndSeries * @ @ S + Share File Edit View Insert Format Tools Add-ons Help Last edit was 1 hour ago 100% Normal text Arial - 11 + B I U A . G PO BEEBE MEE EEX A 31 1 1 1 . 3 1 1 1 7 1 1 1 1 PROBLEM #1 Identify each of the following sequences as finite or infinite. Then classify as arithmetic, geometric, or neither. Finally find an explicit formula (rule for the nth term) for each. Designate the first term with n = 1. Table 1 Example: Infinite 5, 40, 320, 2560, 20480, ... Geometric Formula: 31 =5(8) #-1 a. 4, 8, 12, 16, 20, 24, ... + b. 2b, 4b, 6b, 8b, 10b, 12b, 14b c. 3, -9, 27, -81, ... 1 3 9 27 729 d. 2' 2'2 2 2 e. 1, 4, 9, 16, 25, 36, ... N Consider some of the same sequences written as series. +f8M9X_SequencesAndSeries * @ @ S + Share File Edit View Insert Format Tools Add-ons Help Last edit was 1 hour ago 100% Normal text Arial - 11 + BIUA A 31 1 ' 1 1 1 2 : 3 1 14 1 1 1 | 1 1 15 1 1 1 1 1 1 1 6 1 1 4 1 1 1 7 1 1 1 1 1=3 PROBLEM #2 Write the expanded series represented by the given summation notation. C 2j a. (4i- 3) b. + 3/ - C. PROBLEM #3 Express the series below in summation notation for the specified number of terms. N +f8M9X_SequencesAndSeries * @ @ S Share File Edit View Insert Format Tools Add-ons Help Last edit was 1 hour ago 100% Normal text Times New.. 12 BIUA .. A 31 1 ' 1 11|1 1 12 1 1 1 1 1 1 13 1 1 4 1 1 1 | 1 1 1 5 1 1 1 1 1 1 1 6 7 1 1 1 1 1 1 7 1 1 1 C a. 2 +4+8 + 16 b. 10 + 14 + 18 + 22 + 1 2 3 4 5 c. 2 3 4 57 6 PROBLEM #4 + Add comment When asked to find the sum of, or to evaluate, a series, would you rather it be written in sigma or expanded notation? Is one notation better than the other when the series is very long? Suppose the series is infinite. Explain your answers. PROBLEM #5 Would you change your answer to the above question if there were a shortcut method for N evaluating the sum of a series, rather than adding all the terms? +f8M9X_SequencesAndSeries * @ @ S Share File Edit View Insert Format Tools Add-ons Help Last edit was 1 hour ago 100% Normal text Times New. - 12 BIUA .. A 31 1 ' 4 . 1 1 1 1 5 1 1 1 1 1 1 1 6 7 1 1 1 1 1 1 7 1 1 1 PROBLEM #6 C When asked to describe a series or the relationship between terms of a series would you rather it be written in sigma or expanded notation? PROBLEM #7 Can you represent every series in sigma notation? For example, can the series 1 + 4 + 9 + 61 + 52 be represented in sigma notation? + PROBLEM #8 + What are the advantages and disadvantages of using sigma notation? Write a short paragraph (4-5 sentences) to answer this question. Give examples to support your statements. 2 +