A community for students.
Here's the question you clicked on:
 0 viewing
Loser66
 one year ago
We have
\[\sum_{j =1}^n j = \dfrac{n(n+1)}{2}\]
How about the limit from m to n? I meant
\[\sum_{j =m}^n j=??\]
Please, help
Loser66
 one year ago
We have \[\sum_{j =1}^n j = \dfrac{n(n+1)}{2}\] How about the limit from m to n? I meant \[\sum_{j =m}^n j=??\] Please, help

This Question is Closed

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2\[= \sum_{1}^{n}j  \sum_{1}^{m1}j\]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2sorry for lack of notation

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2terms from m to n = nm+1 so summation wuld be \[\frac{ (nm+1)(m+n) }{ 2 }\]

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2number of terms =nm+1 1st term =m and common diff=1 so just put this in the formula of summation of ap :)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0In general, if we see the lower limit is not 1, when we see n, we replace by what? hehehe. I am silly, just want to generalize the formula like \(\sum_{j = 1}^n = \dfrac{n(n+1)}{2} \) the second n+ 1 is upper + lower limit, right? the first n is upper  lower +1 Hence for all lower limit, we just apply it, right?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2can't you apply that in the same way?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0I don't know, I ask and need a confirmation or a logic how to generalize it. Since I don't think we can.

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2\[\sum_{j=m}^{ n}f(j) = \sum_{j=1}^n f(j)  \sum_{j = 1}^{m1}f(j)\]Do you see why the above is true?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2Cool. So it can be generalised, right?

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2Just wondering  are you an Indian?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0ok, got it. the first sum = (n(n+1) )/2 the second sum = ((m1)(m1+1))/2 some algebraic calculation and we get the answer. Thanks a lot No, I am not. I am Vietnamese

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.2sry there was some server update i had to go >.<
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.