real analysis – Given the sequence, how can I show that this series diverges?

I currently have some problems with this math exercise. I have to show that the series $ sum_ {n = 1} ^ infty b_n $ with $ b_n = sum_ {k = n + 1} ^ {2n} frac {1} {k ^ 2} $ diverges.

I think I have problems with this problem because I don't really know how to apply the quotient rule or the comparison test to the given sequence.

Could someone help me a little?

Thank you!

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Changing the calendar of a series event: Google Calendar

I plan my tasks and reminders in the Google calendar.
I have several calendars based on the task category, and 02 of these calendars are "Recurring tasks and events" for recurring tasks and "Completed things", where I move the tasks, once they are finished.

Now, I want to transfer a task (for example, a weekly review task) that is recurring in nature from "Recurring tasks and events" to "Completed things", once completed, for that particular recurring task.
But, when I do, it changes the timing of all the events in the series, including future events, which is not the goal.

While there are certain attributes, for example changing the name of the task to Completed which can be changed for this particular event only.

As far as I can remember, I used to change the calendars for particular events as well in the past, but that doesn't happen now.

I tried it on the official Android app, the website and the Ubuntu client, with the same result.

So how do we get there?

sequences and series – Show that an explicit formula for $ u_r $ is given by $ u_r = 1+ frac {10} {3} [4^{r-1} -1]$

A sequence $ u_1, u_2, u_3 $, … is such that $ u_1 = $ 1 and $ u_ {n + 1} = 4u_n + 7 $ for $ n geqslant 1 $.

Note the first four terms in the sequence.

I solved the first half of the question.

$ T_1 = $ 1

$ T_2 = $ 11

$ T_3 = $ 51

$ T_4 = 211 $

What kind of sequence is this? It cannot be a geometric progression because there is no common relationship, nor can it be an arithmetic progression since 39; there is no common difference.

I need help solving the second half of the question.

Show that an explicit formula for $ u_r $ is given by $ u_r = 1+ frac {10} {3} [4 ^ {r-1} -1] $

How to show it? Should I use the formulas given in the question? Where is it $ u_r = S_r – S_ {r-1} $?

Creation of an EXE test using a series of NUnit classes

I have a series of NUnit test classes configured in VS2019 Community Edition I need to build an EXE so that they can be run anywhere. I tried to build the EXE in VS and I don't see the executable. These were performed using selenium C # in VS.
What is the correct way to configure this correctly?

are exponential – Is this series equation always true

Hi everyone, is this still true?

According to my limited survey (via value substitution), this seems to be true when n gets bigger.

My limited knowledge of mathematics led me to believe that

$$ n rightarrow infty, f (n) rightarrow k $$

$$ f (n) = log_n ( sum_ {r = 1} ^ {k} n ^ {r}) $$

$$ f (n) about n $$

modify: corrected $ f (n) rightarrow n $ at $ f (n) rightarrow k $

A finite trigonometric series

What is the value of $$ cos {x} + cos {1 + x} + cos {2 + x} + … + cos {359 + x} $$ ?

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sequences and series – Sum of sub-sequences of fibonacci numbers

I read an interesting question here yesterday Sums of sub-sequences of the Tribonacci number. It turns out that if you have two sub-sequences of Tribonacci numbers that have the same sum, you generally cannot move the indices and keep the equality invariant. But I was wondering, since there are more "small" numbers in the Fibonacci sequence, is it the same for Fibonacci numbers. I wrote a quick program to check for small counterexamples, but it seems to be true. I don't see any way to prove it directly proves it. There could be certain properties of the Fibonacci sequence that must be proven first. Any help is appreciated.