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Solved Problems on Introduction to Sequences. Solved Problems on Introduction to Sequences by Mika Seppälä Sequences Definition A sequence ( a n )=( a.

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Presentation on theme: "Solved Problems on Introduction to Sequences. Solved Problems on Introduction to Sequences by Mika Seppälä Sequences Definition A sequence ( a n )=( a."— Presentation transcript:

1 Solved Problems on Introduction to Sequences

2 Solved Problems on Introduction to Sequences by Mika Seppälä Sequences Definition A sequence ( a n )=( a 1, a 2, a 3, … ) is a rule that assigns number a n to every positive integer n.

3 Solved Problems on Introduction to Sequences by Mika Seppälä 1 SEQUENCES (3., 3.1, 3.14, 3.141, ,…) 2 3 Find the general rule defining the following sequences.

4 Solved Problems on Introduction to Sequences by Mika Seppälä 4 SEQUENCES Let n be a positive integer. Define the sequence ( s k ) by Let n = 3, compute ( s k ).

5 Solved Problems on Introduction to Sequences by Mika Seppälä 1 SEQUENCES Solution The denominators are Answer The general n th term is. 1, 2, 6, 24,… = 1, 21, 321, 4321,…

6 Solved Problems on Introduction to Sequences by Mika Seppälä 2 SEQUENCES Solution Remember Answer (3., 3.1, 3.14, 3.141, ,…) The general n th term is n first numbers in the decimal point expansion of

7 Solved Problems on Introduction to Sequences by Mika Seppälä 3 SEQUENCES Solution Clearly Answer for some f. f(1) = 1, f(2) = 2 2,f(3) = 9 = 3 2,f(4) = 16 = 4 2.

8 Solved Problems on Introduction to Sequences by Mika Seppälä 4 SEQUENCES Let n be a positive integer. Define the sequence ( s k ) by Let n = 3, compute ( s k ).

9 Solved Problems on Introduction to Sequences by Mika Seppälä 4 SEQUENCES Solution Answer


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