Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 384316: Find the missing number: 5, 8, 6, 4, 4, 0, 8, ?
I tried 3n-1. I started with n=2,then n=3, but it failed at n=4.
I also tried the multiple of the difference of the numbers. the difference between 5&8 is 3, then multiply that by the difference between 8&6 which is 2; so (5-8)* (8-6)= 6. Then (8-6) * (6-4)=4, then (6-4) * (4-4)=0
That's where it failed.
I also tried 2n-1 starting with n=3, but that failed also.
I looked for a pattern in the difference between the numbers, like the triangular numbers or Fibonacci numbers but no luck.
I don't know what else to try.
Click here to see answer by richard1234(7193)   |
Question 384386: Hi Please help,
Obtain the Maclaurin series expansion about the point 0 for the function ln(x+1) as
ln(x + 1) = x-x^2/2+x^3/3+(1)^n+1x^n/n + ...
Note that we cannot find a Maclaurin expansion of the function ln x since ln x does not exist at x = 0 and so
cannot be differentiated at x = 0.
Thank You in advance
Matt
Click here to see answer by richard1234(7193) |
Question 386226: Hi! I have a couple of questions I need help with so I would love for step-by step solutions. Thanks!
1. Find he sum of the integers between 1 and 100 which are not divisible by 3
2. Three consecutive terms of an arithmetic sequence have a sun of 12 and a product of -80. Find the terms.
3. Each year a sales-person is paid a bonus of $2000 which is banked into the same account which earns a fixed rate of interest of 6% p.a. with interest being payed annually. The amount at the end of each year in the account is calculated as follows: A(0) = 2000
A(1) = A(0) x 1.06 + 2000
A(2) = A(1) x 1.06 + 2000 etc.
Find the total bank balance after 10 years. Assume no fees or charges
4. A ball takes 1 second to hit the ground when dropped. It then takes 90% of this time to rebound to its new height and this continues until the ball comes to a rest.
a. Show that the total time of motion is given by 1+2(0.9)+2(0.9)^2+2(0.9)^3...
b. Find S(n) in for the series in the set given in a.
c. How long does it take for the ball to come to rest?
Sorry for all the questions. There are four and the last one has three sub-problems. I really appreciate all the help!
Click here to see answer by solver91311(24713)  |
Question 386743: you are training for a triathlon. In your training routine each week, you bike 5 times as far as run and run 4 times as far as you swim. one week you trained a total of 200 miles. how many miles did you swim that week?
Click here to see answer by mananth(16946)  |
Question 387127: write an algebraic expression that represents Sn for each expression and find the ninth term of each sequence:
1.) {12,6,3,1.5,..}
2.) {1/2,1/3,1/4,1/5,..}
3.) {1,-2,3,-4,..}
Click here to see answer by richard1234(7193) |
Question 388210: I am supposed to add a sequence of numbers starting with one and going to number thirty. I have added them together and I got 465 as an answer. They want me to write a formula showing this. I don't know what to do next. I think it is something like 1+2+3...=30. but I am not sure.
Click here to see answer by robertb(5830)  |
Question 388365: a question on the homework i have says: Let the sum of an arithmetic sequence of eight terms be represented by the letter S. If the first term is "a" and the eighth term is "a/2" express "a" as a function of S.
Click here to see answer by stanbon(75887) |
Question 386839: Two cakes, A and B, weigh 15 kg altogether. If 1/3 of cake A and 1/4 of cake B are sold, the remaining part of cake A is 1/5 kg less than the remaining part of cake B. If cake A weighs x kg, form an equation in x and solve.
Click here to see answer by robertb(5830) |
Question 386742: you are training for a triathlon In your training routine each week you bike 5 times as far as and you run 4 times as far as you swim One week you trained a total of 200 miles how many miles did you swim that week?
Click here to see answer by robertb(5830) |
Question 389284: Let the function f be defined by y = f(x), where x and f(x) are real numbers.
f(x) = 4x + 10
Find the following. (Simplify your answers completely.)
f(2)= _____________
f(-3)= _____________
f(k)= _____________
f(k^2-1)= _______________
Click here to see answer by richard1234(7193) |
Question 389284: Let the function f be defined by y = f(x), where x and f(x) are real numbers.
f(x) = 4x + 10
Find the following. (Simplify your answers completely.)
f(2)= _____________
f(-3)= _____________
f(k)= _____________
f(k^2-1)= _______________
Click here to see answer by ewatrrr(24785)  |
Question 389732: consider the function f(x) = (x - 3)^2 + 2. Evaluate a sum to approximate the area under the curve for the domain o < or equal x < or equal 2 using the type of rectangles in each part.
a.) use inscribed rectangles 0.5 units wide
b.) Use circumscribed rectangles 0.5 units wide
Click here to see answer by richard1234(7193) |
Question 390924: Domenik has a coin bank in which he saves only P1 coin and 5 coins. When the coin bank was full, he asked his father to open it for him and asked to count how much money was in it. His father told him that all in all Domenik was able to save p238 and there were 66 coins all in all. How many P1 and 5 coins where there in the coin bank?
Click here to see answer by mananth(16946) |
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