Finding the General Term of a Series

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SUMMARY

The discussion focuses on finding the general term of the series defined by the sequence 1, 1*4, 1*4*7, and so on. The proposed solution suggests that the nth term can be expressed as Term(N) = Term(N-1) * (3N-2), which simplifies to (3N-5)(3N-1) = 9N^2 - 18N + 5. However, this solution is incorrect as it fails to account for the increasing number of factors in each term. The correct approach requires identifying a formula that incorporates all factors up to the nth term.

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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?
 
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smart_worker said:

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##.
 

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