Please help me. Number 1.0.3.4.13.12.39 The general term formula of If possible, please write the derivation
Let it be a U n
The questions are:
A_ 4 - A_ 2 = 4; A_ 6 -A_ 4 = 8; ==>
A_ 2*n+2 -A_ 2*n = 4*2^(n-1) ===>
A_ 2*n = 4*(2^n -1); n = 1,2,3.
A_ 3 - A_ 1 = 3 - 1 = 2 = 1+1 = 1^2 +1;
A_ 5 - A_ 3 = 13 - 3 = 10 = 9+1 = 3^2 +1;
A_ 7 - A_ 5 = 39 - 13 = 26 = 25+1 = 5^2 +1; ==>
A_ 2*n+1 - A_ 2*n-1 = (2*n - 1)^2 +1; ==>
A_ 2n+1 = n + 1 + n*(4*n^2-1)/3; n = 0,1,2.
To sum up, a_ N = 0
When n is even
When n is odd