Finding the General Term of a Series

AI Thread Summary
The discussion focuses on finding the general term of the series 1 + 1*4 + 1*4*7 + ... and testing its nature. An initial attempt suggests that the nth term can be expressed as Term N = Term (N-1) * (3N-2), leading to a quadratic expression. However, it is pointed out that this approach is incorrect because each term in the series contains an increasing number of factors. The correct formulation should involve a product that reflects the pattern of the series, indicating that a more complex formula is needed for the nth term. The conversation emphasizes the importance of accurately capturing the series' structure in the general term.
smart_worker
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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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