The problem suggests a finding of a sum of even terms of Fibonacci sequence:

S=2+8+34+... (+all even numbers less than 4000000)

This problem can be easily solved by using a general term formula for Fibonacci sequence and by using a formula for a sum of geometric progression.

By the way. Thank you for the problem. It will be a good task for my students.

Thanks Bertran,

So the number would be:
0, 2, 8, 34, 144, 610, 2584, 10946, 46368, 196418, 832040, 3524578

and the SUM is: 4613732 ?

Am I correct? (just tell me am I correct or not )

This is a cheating. But anyway, your result is correct.

It is very strange. It is interesting to hear another persons and how they did understand this problem.

Make sure there isn't any whitespace (tabs, spaces, etc) surrounding your answer. I can confirm that 4613732 is the correct answer, since I solved that problem years ago.

(November 21, 2011 at 2:59 pm)Bertran Wrote: This problem can be easily solved by using a general term formula for Fibonacci sequence and by using a formula for a sum of geometric progression.

Just out of curiosity, what are the relevant formulae? (Not a student, just a middle-aged guy that's been out of math of a long time)

(November 21, 2011 at 4:49 pm)Cthulhu Dreaming Wrote: Just out of curiosity, what are the relevant formulae? (Not a student, just a middle-aged guy that's been out of math of a long time)

Of course, I'm talking about this formula for F_n.

(November 21, 2011 at 5:17 pm)Bertran Wrote:

(November 21, 2011 at 4:49 pm)Cthulhu Dreaming Wrote: Just out of curiosity, what are the relevant formulae? (Not a student, just a middle-aged guy that's been out of math of a long time)

Of course, I'm talking about this formula for F_n.

Thanks. Interesting, yet (somewhat) incomprehensible, as my math education ended at high-school trigonometry. One of these days, I'll have to figure out that high falutin' math stuff.