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When p>1 converges

Diverges when 1≥p

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k=∞

Converges if and only if

1) lim a_n = 0

   n→∞

2) a_n+1≤a_n

Use the ratio test if have n! or xⁿ

do L=lim   l a_n+1 / a_nl

                                n→∞

E(k/factorable polynomial)

do partial fractions and then usually BUT NOT ALWAYS have to break into two separate sigma notations

Just switch the sigma with an integral

NOTE: Very often this involves u sub, actually almost always

Remember LIATE

derivative of ln n = 1/n dn

Do lim a_n 

    n->∞

If lim doesn't equal zero series diverges

If lim does equal zero series converges

When series = a + ar + ar²

Converges to S=a/(1-r) if lrl<1

Diverges if lrl≥1

Two series, Ea and Eb

Ea ≤ Eb

If Eb converges, so does Ea

If Ea diverges, so does Eb

If Eb diverges, test is inconclusive