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
ik
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