Say the sequence is: 1,3,6,10,15,21,...
You can see that you are adding 2, then 3,...
Just because you are adding does not make it arithmetic though. In order for it to be arithmetic, the sequence must add or subtract the same number each time. Being that this sequence adds a different number each time, this sequence is not classified as arithmetic or geometric.
Same rules apply for geometric. If it does not multiply by the same number each time, it is not geometric. NEITHER IS ALWAYS A CHOICE.
The limit lesson is very easy so no worries
ReplyDeleteill make it very easy for you so that you can understand it for the test
there are two types of limit equations
the ones that use rules
and the ones that use a calculator
the ones that use rules have simple hints to memorize for solving
the only ones that use rules are the polynomial equations problems
**Every polynomial limit equation will follow a rule
memorize this
((the rules))
t- top lead co
b- bottom lead co
t=b then coefficients
t>b then infinity
t<b then zero
if you get a problem with a limit that is a polynomial equation
use the rules.
each and every time
the other type of problem is the one that calls for the use of a calculator
**every problem with limits that is not a polynommial equation calls for the use of a calculator
all you have to do is plug in for n three different times with
100
1000
10000
then plug into calculator
record what each outcome is
and decipher what the numbers are headed toward which will then be your answer
if my hints confuse you just talk to me and ill help
And when taylor says the top and bottom coefficients are equal to each other you take those two and the fraction is the answer.
ReplyDeleteEx:
(7^2+3)/(2^2+5)
take the highest coefficient from the top and bottom (7^2 & 2^2) and your answer is 7/2
To elaborate on what a limit is, It is a series of numbers that approaches something without ever reaching it. Limits can approach 0, infinity, 1, 1/2 or any number. Also, beware of rounding when plugging into your calculator! Most calculators will only float 10-20 decimal places and will begin rounding as you plug bigger numbers into the limit.
ReplyDeleteThe limit approaches the number but never reaches it and there are a few rules when dealing with limits:
ReplyDelete1. if the degree of the top number=degree of the bottom number then the answer is the coefficients
2. if the degree of the top is > the degree of the bottom then it = infinity
3. if the degree of the top is < the degree of the bottom then it = 0
if the place number isnt asked for then that probably isnt what you are looking for
ReplyDeletereview what each variable represents
tn= an actual number
n= the "address" of a number
dont get that confused
so if a problem doesnt specify an "n" essentially you are looking for a simple formula to figure out what the Tn would be for a specific address of a series
basically youre using the formuala you have memorized to make up a formula to find the tn for any address of that specific equation