Finding the General Term of a Series

[smart_worker]

Homework Statement

Find the general term and test the nature of the series:

Homework Equations

1+1*4+1*4*7+...

The Attempt at a Solution

Term N = Term (N-1) * 3N-2

Hence,3(N-1)-2 * 3N-2

which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5

Is this correct?

 

[LCKurtz]

Homework Statement

Find the general term and test the nature of the series:

Homework Equations

1+1*4+1*4*7+...

The Attempt at a Solution

Term N = Term (N-1) * 3N-2

Hence,3(N-1)-2 * 3N-2

which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5

Is this correct?

No. Each term of your series has one more factor in it. So the nth term would have to written like$$
a_n = 1\cdot 4 \cdot 7 ...(\text{something involving }n)$$where that "something" is a formula for the last factor of $a_n$.