Re: nth term of a Series when d is not constant

Jeff nous a récemment amicalement signifié : 
Hi All,

I have a Series (is this the correct name when the difference is not
constant?) that progresses as follows:

2i, where i is the iteration.

For example, starting at 1:

1,3,7,13,21,31

3 - 1 = 2
7 - 3 = 4
13 - 7 = 6
...

Can the nth term be calculated as in standard arithmetic series?

Hello Jeff

Sure :
u_n     = u_(n-1) + 2n
u_(n-1) = u_(n-2) + 2(n-1)
....
u_1     = u_0     + 2*1
u_0 = 1

Summing all these equalities :
u_n = 1 + 2(n + (n-1) + (n-2) + ... + 1)
u_n = 1+n(n+1)

So, u_n=n^2 + n + 1 is your response.

--
Patrick

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