Calc BC Chapter 9 Formulas

If bot grows faster than top, lim= _____

0

A geometric series w |r|>1 will _____ A geometric series w 0<|r|<1 will _____

Diverge Converge to a/1-r

If a sequence {an} is bounded & monotonic, then _____

It converges

lim n➡️∞ an= L, lim n➡️∞bn= K lim n➡️∞ (an+bn)= _____ lim n➡️∞ (anbn)= _____ lim n➡️∞ (can)= _____ lim n➡️∞ (an/bn)= _____

L+K LK cL, c is any real # L/K, bn & K not = 0

Sequence {an} bounded above if... Bounded below if... Bounded if...

Real # M such that an ≤ M for all n Real # N such that N ≤ an for all n Bounded above & below

What is the nth partial sum?

Sum of the 1st n terms of an infinite series

Relative growth rates of various functions (_____ constant)

nn FEPL constant (fast➡️slow growth): n^n Factorial Exponential Polynomials/powers Logarithms Constant

If ∑an converges,

{an} converges to 0

If {an} DOES converge to 0, If {an} does NOT converge to 0,

∑an may or may not converge ∑an will NOT converge