General term of a series

  • #1
smart_worker
131
1

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?
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,568
774

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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