Choosing Between the Ordinary & Limit Comparison Test

[rcmango]

Homework Statement

First questions is: How to choose between using the ordinary comparison test, or using the limit comparison test?

Homework Equations

The Attempt at a Solution

then, for these two problems below, i decide to use the limit comparison test:

SUM n_infinity (3n - 2)/(n^3 - 2n^2 + 11) then its said to look for the largest degree of terms in the numerator and denominator and divide through which is to divide by: 3/n^2

but why is 3/n^2 the largest term, when there is a n^3 in there, why not 3/n^3 ?

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also, i see that 1/n belongs to the harmonic series, but what series does 3/n^2 belong to?

thankyou.

 

[Dick]

Because the relevant term in the numerator is 3*n. 3*n/n^3=3/n^2.