Investin Sequence

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    レポート理工学数学数列考察

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    数学理工学

    資料紹介

    From the question above, we can see that for n = 1, we will get 1 x 1! by the equation.
    And for n = 2, we have 2 x 2! and identically, we have 3 x 3!, when n = 3. There is a simple pattern.
    So, we can understand that the n x n! is the formula for the nth term of the sequence.

    From the Part 2’s examples, we actually couldn’t figure out the pattern of the sequence,
    because it’s not a simple arithmetic or geometric sequence.

    So, what I did was I randomly tried some factorials and some equations, which seems related.
    The lists are in below.

    資料の原本内容( この資料を購入すると、テキストデータがみえます。 )

    @ Investigating a Sequence of Numbers.
    PART 1. The sequence of numbers { an }∞n=1 is defined by,
    a1 = 1 x 1! a2 = 2 x 2! a3 = 3 x 3! …
    Find the nth term of the sequence. From the question above, we can see that for n = 1, we will get 1 x 1! by the equation.
    And for n = 2, we have 2 x 2! and identically, we have 3 x 3!, when n = 3. There is a simple pattern. So, we can understand that the n x n! is the formula for the nth term of the sequence. PART 2. Let Sn = a1 + a2 + a3 + … + an. Investigate ..

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