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Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4
 5 months ago
 5 months ago
Is there a limit in this progression? 1.1 + 2.1 + 2 + 3.1 + 2 + 3 + 4
 5 months ago
 5 months ago

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osansevieroBest ResponseYou've already chosen the best response.1
Infinite? and how to demostrate it?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
which progression is the sequence in ?
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
The question: 1. Determine if the next sequence has a limit (demostrate it) and determine it (hint:find the general term) c) 1,1 + 2,1 + 2 + 3,1 + 2 + 3, + 4...
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
I cant find any order...
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
each term is just the sum of '1st n natural numbers'
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
thats your general term \(a_n =n(n+1)/2\)
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
how do you find whether next sequence has a limit ?
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
Why is that the general term?
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
a1=1(1+1)/2=2/2=1 Does not apply...
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
1st term is indeed 1 right ? 1, 1+2 , 1+2+3 , .... 1,3,6, 10,...
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
and each term is sum of 1st n natural numbers 1st term = 1 2nd term = sum of 1st 2 natural numbers =1+2 =3 and so on
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
Oh...now I understand! Give me a minute
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
Cant you add the series plus iteslf? like this: Sn= 1 + 3 + 6 + 10 + ... + n2 + n1 + n Sn= n + n1 + n2 +...+ 6 + 3 + 1
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
So: 2Sn= (n+1) + (n+2) + (n+4)...ehm...this is not going right
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
so you want to find the sum ?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
\(\Large (1/2)\sum (n^2+n) = (1/2)\sum n^2+(1/2)\sum n=...?\)
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
Oh...I thought that I could add Sn + Sn, and then divide them by two to get the general term
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
possible but i don't think its that easy....
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
then how to get the limit?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
how do you find whether next sequence has a limit ? i may know it, but not in these "limit of next sequence" terms ...
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
When it says "the next sequence" it refers to the one I put
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
ok, so you just want to find whether the sum converges or not ?
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
Look, I have 5 exercises 1. \[\left( 1 \right)^{n}\left( \frac{ 5n+4 }{ 2n } \right)\] For this one we saw that the 4 will be nothing in comparison so the limit without the 1n is 5/2. It has no limit because it is ocilating. 2. \[2^{1}\times2^{2}\times2^{3}...\] Because there is a negative sign, it will change, so there is no limit
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
What means converges?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
sum converge means sum = finite
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
I want to know if it has a limit and to demostrate and determine it. I think that for this infinite is the limit, am I right?
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
How did you wrote the general term? Is there a mathematical way to get it?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
the sum of 1st n natural numbers ? that you can find by your method, Sn = 1+2+3+....n Sn = n+n1 +n2 +...3+2+1 2Sn = (1+n)+ (1+n) +..... so, each pair sum is (1+n) and there are n terms so, 2Sn = n (n+1)
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
so, sum of 1st n natural numbers = n (n+1)/2
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
that became your general term and for your sequence, you need to sum this, and whne n becomes large the sum goes on increaseing which menas this progression has no limit.
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
\[an?\left\{ an=\frac{ 1 }{ 2 }\left( a _{n1} + \frac{ 10 }{ a _{n1} }\right) \right\} for n \ge2\]
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
have you solved such problems, with a (n1) , before.... because i just could think of finding, a1,a2,a3...and see whether there's any pattern...
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
but I dont have a1
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
this is just telling you that the new value is the last one added by 10 divded by iteslf \[\left( a ^{2} +\frac{ 10 }{ a ^{2} }\right)\] divided by two
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
yes, i though it was already given....
 5 months ago

osansevieroBest ResponseYou've already chosen the best response.1
So can it be determined with the things given?
 5 months ago

hartnnBest ResponseYou've already chosen the best response.1
i am not sure about this....can you ask in new post so that others can try.....sorry.
 5 months ago
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