Investin 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.
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.
@ 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 ...
