SOLUTION: Find the sum of the first n terms of the following series 3X1^2 X5X2^2+7X3^2+---

Question 984368: Find the sum of the first n terms of the following series
3X1^2 X5X2^2+7X3^2+---

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I believe what you really need to calculate is

Once you figure out that formula,
can be proven by induction, like this:
1) The formula is true for .
For ,
and the formula ,
which tells us that
,
which makes the formula true tor .
2) We can prove that if were true for any whole number, it would be true for .
Term number is
.
If , then

=
and that show that the formula is true for , because the formula says that

=
=
=
=

HOW WE CAN GET TO THAT FORMULA:
The sum of terms are of the form with is a polynomial of degree in with no independent term.
,
, and so on.
So, the sum of terms of the form should be

Knowing that
,
,
, and
,
we can find , , , and by solving

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