Please solve it

[nagaprasady]

Modelling: Post on social media website has received these numbers of comments. predict how many comments the post after 25 days.

Day 1 - 225 comments
Day 2 -450 comments
day 3-775 comments
Day4 -1200 comments

find an expression for n days based on sequence

Please advise on it

[Guest]

It is an arithmetic progression
d=100
a1=225
n=25

a25=a1+(n-1)d=225+24*100 = 225+2400 = 2625

More info https://www.math10.com/en/algebra/arith ... ssion.html

[Guest]

Please solve

[HallsofIvy]

Please solve

One of the difficulties with not requiring registration is that so many people are called "guest"" and it is impossible to tell whether the "guest" who posted this completely different question is the same "guest" who posted the first or a completely different person who has "hijacked" this thread!

In any case, this last post is complete non-sense! I suppose the first part, referring to Fourier series is related to the question of the numeric sum but that question asks us to show that the sum on the left, which has no dependence on n, is equal to a fraction with [tex]n^2[/tex] in the numerator!

I might guess that, this is NOT an infinite sum as it appears but rather a sum to "n" That is:
[tex]1+ \frac{1}{3^2}+ \frac{1}{5^2}+ \cdot\cdot\cdot+ \frac{1}{(2n+1)}[/tex].

But that can't be right! Taking n= 0 on the left gives 1 but [tex]\frac{n^2}{8}= 0[/tex]. Taking n= 1 on the left gives [tex]1+ \frac{1}{9}= \frac{10}{9}[/tex but [tex]\frac{n^2}{8}= \frac{1}{8}[/tex]. Taking n= 2 on the left gives [tex]1+ \frac{1}{9}+ \frac{1}{25}= \frac{259}{225}[/tex], not [tex]\frac{2^2}{8}= \frac{4}{8}= \frac{1}{2}[/tex].