Hi-Sec Mymen 2008 4

Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
User avatar
rakeen
Posts:384
Joined:Thu Dec 09, 2010 5:21 pm
Location:Dhaka
Hi-Sec Mymen 2008 4

Unread post by rakeen » Sat Dec 11, 2010 4:20 pm

1. What is the sum of this progression upto 10th term: 7+5+12+17+29+46+...

MySol: if we take this way: 7+5+(7+5)+(7+5+5)+(7+5+5+(5+7))...... we might solve the prob. My ans in 825. What abt yours?
r@k€€/|/

tushar7
Posts:101
Joined:Tue Dec 07, 2010 3:23 pm

Re: Hi-Sec Mymen 2008 4

Unread post by tushar7 » Tue Dec 14, 2010 12:56 am

so we can generalize this

$f_n=f_{n-1}+f_{n-2}$

User avatar
rakeen
Posts:384
Joined:Thu Dec 09, 2010 5:21 pm
Location:Dhaka

Re: Hi-Sec Mymen 2008 4

Unread post by rakeen » Tue Dec 14, 2010 3:45 pm

can u post me the solution. I've done this before, but last day I tried this and couldn't make it! And how can I find the $f$ _n-1
r@k€€/|/

User avatar
Moon
Site Admin
Posts:751
Joined:Tue Nov 02, 2010 7:52 pm
Location:Dhaka, Bangladesh
Contact:

Re: Hi-Sec Mymen 2008 4

Unread post by Moon » Sun Jan 16, 2011 9:52 pm

This is nothing but Fibonacci Series with different starting terms. BTW for $10$ terms, we don't need to do anything fancy. It is enough to list them and add them. :)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

Dipan
Posts:158
Joined:Wed Dec 08, 2010 5:36 pm

Re: Hi-Sec Mymen 2008 4

Unread post by Dipan » Sat Jan 22, 2011 11:06 pm

In the series the 7th term is 46+29 = 75....so, the sum of the series upto 10th term is 75*11 = 825.

AntiviruShahriar
Posts:125
Joined:Mon Dec 13, 2010 12:05 pm
Location:চট্রগ্রাম,Chittagong
Contact:

Re: Hi-Sec Mymen 2008 4

Unread post by AntiviruShahriar » Sun Jan 23, 2011 4:48 pm

Dipan wrote:In the series the 7th term is 46+29 = 75....so, the sum of the series upto 10th term is 75*11 = 825.

eita ki k0no generalized formula???
R kmne h0ilo eita :?:

protik
Posts:35
Joined:Wed Dec 08, 2010 7:21 am

Re: Hi-Sec Mymen 2008 4

Unread post by protik » Sun Jan 23, 2011 7:28 pm

what is the rule to get the sum of n series in a fibonacci series..??

Dipan
Posts:158
Joined:Wed Dec 08, 2010 5:36 pm

Re: Hi-Sec Mymen 2008 4

Unread post by Dipan » Sun Jan 23, 2011 11:35 pm

@Anti...ohh yup.that is a generalized formula.If you want to get the sum of a fibonacci series upto 10th term or any serial 10 term you can get it simply by multiplying the 7th term by 11. Do you want the proof???

@Protik...I think you want to get the sum of a fibonacci series upto nth term.If you want to do so you can do it using this formula

sum of fibonacci series upto nth term(Fn) = Fn+2 - 1

AntiviruShahriar
Posts:125
Joined:Mon Dec 13, 2010 12:05 pm
Location:চট্রগ্রাম,Chittagong
Contact:

Re: Hi-Sec Mymen 2008 4

Unread post by AntiviruShahriar » Mon Jan 24, 2011 1:29 pm

Dipan wrote:@Anti. Do you want the proof???
yup...

Dipan
Posts:158
Joined:Wed Dec 08, 2010 5:36 pm

Re: Hi-Sec Mymen 2008 4

Unread post by Dipan » Tue Jan 25, 2011 5:56 pm

@Anti...I am giving you hint. First try to do it yourself.If you can't then I shall give you the proof.
For a fibonacci series you can write, Fn + F n+1 = F n+2
and you have to prove,
F n + F n+1 + F n+2 .....................F n+9 = 11 F n+6.
Ok..

Post Reply