Question

@whpalmer4 I had 12 problems and I did 8 of them. However there's 4 of them I need help with :/

1)What is a recursive definition for the
sequence 3, 5, 9, 17, 33 . . . ?
Identify how the terms change from one
to the next.

6
2) Σ n^2+1 What is the sum of the series?
n=1

3) 5
Σ 16(1/4)^n What is the sum of the series?
n=0

4) Does the series 1/4-1/2+1-2+....converge or diverge? If it converges, find the sum.

Answer 1

@whpalmer4 there is someone need your help. Please :)

Answer 2

@raquel_mendoza whpalmer4 is sleeping, when waiting for him, let me give you the answer for the first one
let start from the second number:5
5 = 3 + \(2^1\) where 3 is the first number + \(2^{"first"}\)
now , the third one : 9
9 = 5 + 4 = 5 + \(2^2\) , you see, the third one = the second one + \(2^{second}\)
now the 4th one: 17
17 = 9 + 8 = 9 +\(2^3\) , you see, the 4th one = the third one + \(2^{"third"}\)
try one more, the 5th one: 33
33= 17 + 16 = 17 + \(2^4\) = the 4th one + \(2^{"forth"}\)
so the recursive formula is
\[a_n = a_{n-1}+ 2^{n-1}\]
I don't know whether it is right or wrong, we have to wait for @whpmalre4

Answer 3

@loser66 Alright, I think I understood the pattern! However, I am still confused because these are all "Find the Error" Problems. And as I am looking at the old worksheet, I can't find their error because their work confused me. Maybe I can try posting the sheet because I really want to understand this. Btw thank you for responding :)

Answer 4

http://assets.openstudy.com/updates/attachments/51945e4ee4b0d270317f72d7-melidalkae-1368678016525-chapter9findtheerrors1.pdf

It's the second problem on the first page. I don't understand what did they do wrong.

Answer 5

the error at \(a_n = -3n^2 +4\) the square is just for n only. When computing, they put square for both -3, so that, it goes wrong.
for the first one, for example, n =1 , \(a_n = -3 (1)^2 +4 = 1\)
got what I meant?

Answer 6

Oh no, that's for the first problem! lol I got that one. Number 2, the one next to it starting with "What is a recursive definition for the
sequence 3, 5, 9, 17, 33 . . . ?
Identify how the terms change from one
to the next.

Answer 7

For number 2(first page) on the link, I don't get what was the error for that problem.

Answer 8

the wrongness at the recursive formula itself. It is not correct to say \(a_{n+1} = 3 + 2^n\)
let pick n = 2, so the number is \(a_{2+1}= a_3\) and this guy on the line is 9 , according to its formula, this guy 9 = 3 + 2^2 = 7???? do you really think that 9 = 7 ? so, the wrongness as I pointed.

Answer 9

Ohh Okay! That makes total sense. 9 and 7 are obviously not equal to each other. Thank you so much! Why did the original person put N is greater than or equal to 1? Is that part of the error too?

Answer 10

nope, that's enough

Answer 11

Okay, so the final answer is a(n)=a(n−1)+2^(n−1) with n is greater than or equal to 1?