Convergence of sequence

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Hoshiyomi

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Is the following sequence convergent or divergent?
1623767730313.png with n from 1 -->infinity

I don't know the result but i believe it converge to 1 (i tested with the calculator). I also tried to skew it with another sequence but 1 change inside the parentheses will create a divergent sequence, so basically i failed.

If you have any idea, please share. Thank you in advance!
 
You are asking about the convergence of a sequence but you listed a summation. Which is it?

-Dan
 
A sequence is a list of numbers. Like 1-1/2, 1-1/3, 1-1/4, 1-1/5, 1-1/6, .... where the nth term is 1-1/n. This sequence converges to 1.

However the series [1-1/2]+[1-1/3]+[1-1/4]+.... diverges (every term is at least 1/2)
 
Note that the question doesn't ask for the value of the summation. Therefore, just try to prove that it converges or diverges (we suspect that it converges due to your calculator result). Perhaps try one of the following methods, and try to pick one that you've been taught convergence tests (Wikipedia link). Please post back with your work if you have trouble with this.
 
Hoshiyomi said:
Is the following sequence convergent or divergent?
View attachment 27832 with n from 1 -->infinity

I don't know the result but i believe it converge to 1 (i tested with the calculator). I also tried to skew it with another sequence but 1 change inside the parentheses will create a divergent sequence, so basically i failed.

If you have any idea, please share. Thank you in advance!
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
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