Answer:
Step-by-step explanation:
One is given the following function:
One is asked to evaluate the function for 
, substitute 
in place of 
, and simplify to evaluate:
A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:
Where (
) is the evaluator term (
) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,
Answer:
1:2 - one dog to two cats.
Answer:
1st problem:
Converges to 6
2nd problem:
Converges to 504
Step-by-step explanation:
You are comparing to 
You want the ratio r to be between -1 and 1.
Both of these problem are so that means they both have a sum and the series converges to that sum.
The formula for computing a geometric series in our form is 
where 
is the first term.
The first term of your first series is 3 so your answer will be given by:
The second series has r=1/6 and a_1=420 giving me:
.
Rationalizing is just simpllifying, so the simplified value has the same value as the original expression.
Given:
The given expression is:
To find:
The value of the given expression at 
.
Solution:
We have,
Substituting , we get
![\dfrac{3\sin (-45)-4\sin [4(-45)]}{\sin [5(-45)]}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5Csin%20%28-45%29-4%5Csin%20%5B4%28-45%29%5D%7D%7B%5Csin%20%5B5%28-45%29%5D%7D)
On substituting 
, we get,
Therefore, the value of the given expression at is 
.
