Pre Calc

posted by .

Write as a series and express as a rational number:

1. 5.36363636....

2. 0.0123123....

Use this series and find S1,S2,S3,S4,Sn, and lim Sn.

1/1*3 + 1/3*5 + 1/5*7+...+ 1/(2n-1)(2n+1)

• Pre Calc -

It works easier to have one type problem per question, as you will see here.
On the first, try something like multiping by a power of ten that will align digits. For instance, in the first, multiply by 100
536.36363636 . Subtract the original number
536.3636-5.363636= 531
Now divide by 99 (think out why)

• Pre Calc -

I would split it this way:

5.36363636....
= 5 + (.36 + .0036 + .000036 + ...}

so for the bracket part, a=.36, r = .01

remember S = a/(1-r)

= .36/(1-.01) = .36/.99 = 36/99 = 4/11

then 5.36363636.... = 5 4/11 or 59/11

do the rest the same way

• Pre Calc -

1. 5.36363636.... = 5 + 0.36(1 + 10^-2 + 10^-4 + ..)
= 5 + 0.36[1/(1-.01)]
= 5 + 0.36 * 100/99
= 5 + 36/99

2. Do it the same way

3. If you are dealing with sums, the first term is
S1 = 1/3
and the second term is
S2 = 1/3 + 1/15 = 6/15
Do the others and see what Sn and the limit are

• Pre Calc -

1/1*3 + 1/3*5 + 1/5*7+...+ 1/(2n-1)(2n+1)

S1 = 1/3
S2 = 1/3 + 1/15 = 6/15 = 2/5
S3 = 2/5 + 1/35 = 15/35 = 3/7

do you see a pattern?
so what is Sn ?

An interesting question now would be,

Similar Questions

1. Math

Using the index of a series as the domain and the value of the series as the range, is a series a function?
2. Algebra

Using the index of a series as the domain and the value of the series as the range, is a series a function?
3. calc.

find the sum of the series of (-2)^n/3^n+1. This is an alternating series... what if we rewrite it as an= (1/3)* (-2/3)^(n) Divide any nth term by the n-1 term and see if you get a ratio term r. This might be a geometric series.
4. Calc 2 taylor series

use the definition of a taylor series to find the Taylor series (centeredat c) for the function. f(x)= 7/x c=1 so what is f(x) as n goes from 0 to infinity?
5. Calculus

a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure to show the general term of the series. b) Find the radius of convergence of the series. c)Use Lagrange's Remainder Theorem to prove that for x in the interval of …
6. Calc II

Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4-sin n) / ((n^2)+1) and the series from n=1 to infinity of (4-sin n) / ((2^n) +1). For each series which converges, …
7. Math

the series a_n doesn't have a limit. prove that the series (1/n) doesnt go to 1. use the definiton of lim: for every epsilon>0......
8. Pre-Calculus

Q.Determine the sum of each infinite geometric series. t_1= 8 r = -2^1/2 ---------------------------------------- A.This is a divergent series because the absolute value of r is greater than 1. ---------------------------------------- …
9. Algebra 2

I need steps on how to complete this please i am so confused and lost. :( Consider the infinite geometric series x e n=1 -4(1/3) n-1. In this image, the lower limit of the summation notation is "n=1". a. Write the first four terms …
10. Integral Calculus

We can use this power series to approximate the constant pi: arctan(x) = (summation from n = 1 to infinity) of ((-1)^n * x^(2n+1))/(2n+1) a) First evaluate arctan(1) without the given series. (I know this is pi/4) b) Use your answer …

More Similar Questions