Hi-Sec Mymen 2008 4
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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.
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.
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?
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€€/|/
Re: Hi-Sec Mymen 2008 4
so we can generalize this
$f_n=f_{n-1}+f_{n-2}$
$f_n=f_{n-1}+f_{n-2}$
Re: Hi-Sec Mymen 2008 4
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€€/|/
Re: Hi-Sec Mymen 2008 4
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.
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Re: Hi-Sec Mymen 2008 4
In the series the 7th term is 46+29 = 75....so, the sum of the series upto 10th term is 75*11 = 825.
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Re: Hi-Sec Mymen 2008 4
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
Re: Hi-Sec Mymen 2008 4
what is the rule to get the sum of n series in a fibonacci series..??
Re: Hi-Sec Mymen 2008 4
@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
@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
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Re: Hi-Sec Mymen 2008 4
yup...Dipan wrote:@Anti. Do you want the proof???
Re: Hi-Sec Mymen 2008 4
@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..
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..