mateforum.ro

Luiza · Posted: Sat Jan 24, 2009 10:23 pm Post subject: Proprietati

1)Suma a oricare $2k+1$ numere consecutive se divide prin $2k+1$ ?
2)Suma a oricare $2k$ numere consecutive se divide prin $2k$ ?
3)Care este forma patratelor perfecte ? (adica cum sunt numerele impare $2k+1$ )
_________________
Humuhumunukunukuapua

alex2008 · Leibniz Joined: 19 Oct 2008 Posts: 464 Location: Tulcea

La 3 vezi aici : http://mateforum.ro/viewtopic.php?t=2747
_________________
. A snake that slithers on the ground can only dream of flying through the air.

Andi Brojbeanu · Posted: Sat Apr 25, 2009 7:17 pm Post subject:

1)Numerele sunt: $x, x+1, x+2, ......, x+2k-1, x+2k$ .
Atunci suma lor va fi egala cu: $x+x+1+x+2+....+x+2k-1+x+2k=(2k+1)\cdot x+(1+2+3+.....+2k-1+2k)=(2k+1)\cdot x+\frac{2k\cdot (2k+1)}{2}=(2k+1)(x+k)\vdots 2k+1$ .
2)Numerele sunt: $x, x+1, x+2, ......, x+2k-2, x+2k-1$ .
Atunci suma lor va fi egala cu: $x+x+1+x+2+....+x+2k-2+x+2k-1=2k\cdot x+(1+2+3+.....+2k-2+2k-1)=2k\cdot x+\frac{(2k-1)2k}{2}=2k(x+\frac{2k-1}{2})$ .
Deoarece $\frac{2k-1}{2}\notin \mathb{N}$ $\Rightarrow 2k$ nu divide $2k(x+\frac{2k-1}{2})$ .

	mateforum.ro Forum Index -> Gimnaziu -> Clasa a 5-a	All times are GMT + 2 Hours
Page 1 of 1