Math TEST sequences and series

what is the formula for a 1 space arith. mean

(x + y)/2

how do you absolutely know a series converges

I can't remember

what are the steps to finding a cubic

I don't know if you can -- other than matrices which is: abcd thing, and plug in n to get a system (so you know it's an^3 + bn^2 + cn + d, right? then you plug in the values you know for n (which you know even if you just have a sequence), and you get a system of 4 equations, then you turn that into a matrix and find the answer by multiplying the inverse matrix by the == matrix)

what is the formula to find the partial sum of a geometric sequence

Sn = (t1(1-r^N !!!!))/(1-r)

what is the second arithmetic formula to find the partial sum of a sequence

Sn = n/2(2t1 + d(n-1)) where D = how much you add by each time

what is the first arithmetic formula to find the nth partial sum of an arithmetic series

Sn = n/2(t1 + tn)

how do you find r for a geometric sequence if you know consecutive terms or d for the same type of arithmetic sequence

divide or find the difference between the two

what is an explicit formula

doesn't rely on the numbers that came before

how do you solve arithmetic partial sum problems when you don't know n

fill in the formula and solve for n-- ultimately with the quadratic formula (or factoring if it's easy)

how do you find quadratic sequences

find the linear, then pllug into the formula (with n-1!!!!) and simplify into an equation

what is the formula for finding quadratic polynomial sequences

for Qn = Q1 + ((s1 +s(n-1))/2)*(n-1)

how do you do the harmonic thing

group it

how do you find what a sequence converges to

if denom > power than num, zero. if denom and num are equal, the ratio of their coefficients. If denom greater than num, but you're also adding something outside the fraction, it's whatever ur adding. If n is the exponent, it's generally 0. If num > denom it doesn't converge

how do you know if a SERIES converges

if it's geometric and the absolute value of r <1

FIND OUT IF YOU NEED TO KNOW HOW TO DO THE CALC STUFF AND THEN PUT IT IN THE QUIZLET

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IF IT'S EVEN OR EVEN ODD (ODD JUST DOESN'T HAVE i) AND UR FINDING THE GEOMETRIC MEAN REMEMBER TO FIND ALL THE PLUS MINUS AND IMAGINARY ONES IF IT SAYS SO

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REMEMBER FOR THE HARD ONES JUT USE YOU CALC TO CHECK IF THEY'RE ARITHMETIC OR GEO, AND PLUG IN TERMS IF YOU HAVE THEIR FORMULA

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remember if you have an angle "from" an arc, it's 1/2 the arc

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remember if you have similar triangles you can make proportions to prove the mean

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remember xy = mean^2 when ur proving

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do arithmetic sequences converge

no

how check convergence

plug huge numbers into calc

how do you solve geometric series where you don't know n

plug in and simplify, then you do logs, use the change of base formula, and then plug into you calculator

how do you solve arithmetic partial sum problems where they give you n values and d and t1 or both t1 and tn

plug into the equation

how do you write the Z thing

put num of terms on top of the Z and n= something on bottom and the formula for n on the right. Then you can find it by plugging into you calc

what is a recursive formula

relates n in the context of n-1

if a series converges, how do you find to what

take the geometric formula for a partial sum, and just do t1/(1-r)

how do you find the arithmetic mean for multiple spaces. for example x,__,__,__, y

the first num plus 1 more than the num of spaces * a variable = last num. So x + 4d = y

what is the explicit form for an arithmetic sequence

tn = t1 + d*(N - 1 !!!) n> or equal to 1 (!!)

what is the explicit formula for a geometric sequence

tn = t1*r^(N - 1 !!!) n > or equal to 1

what is a useful trick to finding explicit formulas for random sequences

try and write it out in a box and write out similar sequences in case it has two parts

how do you find if a geometric SEQUENCE converges

1. just look at it and think it through, and 2. if r is greater than -1 and less than 1

how do you find the geometric mean for multiple spaces. for example x, __, __, y

X* d^3 = y. SO first num times the variable to the power of one more than the num spaces = the last num

How do you write the expanded form of a Z thing

just write out all the terms with + signs

how do you write limits

lim over n-> infinity with tn= formula , and then that all = convergence

what is the formula for a 1 space geometric. mean

xy = r^2 so the plus minus _/xy

do u know the format to write a recursive formula in

yes

how do you solve arithmetic equations where they give you t1 and like t6 but ask for partial sum of s200

you find d by knowing t1 + 5d = t6(or the other one if it's geometric) and then use the formula