Sequences and Series

Problem : Find an explicit formula for the following sequence: 1, 3, 5, 7, 9,....

Problem : Find three explicit formulas for the following sequence: -1, 1, -1, 1, -1, 1,… (Hint: Use trigonometric functions, too).

Solution for Problem 2 >>

a _n = (- 1)ⁿ ; a _n = sin( + nΠ) ; a _n = cos(nΠ) .

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Problem : What is the 11 th term of the sequence a _n = 2n - 6 ?

Problem : Calculate (4i - 5) .

Solution for Problem 4 >>

(4i - 5) = - 1 + 3 + 7 + 11 + 15 + 19 = 54 .

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Problem : Calculate 5(k + 2) .

Solution for Problem 5 >>

5(k + 2) = 5(k + 2) = 5[6 + 7 + 8 + 9] = 150 .

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Problem : Let a _n = 4n ² . What is the sum of the first five terms of a ?

Solution for Problem 6 >>

(4i ²) = 4 i ² = 4[1 + 4 + 9 + 16 + 25] = 220 .

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