Question

Se da tabloul de numere R1 2
R2 2,4,2
R3 2,4,6,4,2
R4 2,4,6,8,6,4,
.
.
.
R200...................................
a) Ce numar se afla in mijlocul ultimului rand?
b)Cate numere contine tabloul?

Answer 1

R1: 2

R2: 2, 4, 2

R3: 2, 4, 6, 4, 2

R4: 2, 4, 6, 8, 6, 4, 2

……………………………..

Rk: 2, 4, 6, …,2k-2,  2k, 2k-2,……, 6, 4, 2; kEN

R200: In mijloc se afla 2•200=400

R200: 2, 4, 6,….398, 400, 398, …., 6, 4, 2

Observam ca pe fiecare rand sunt 2k-1 termeni

R1; k=1; 1 termen

R2: k=2; 3 termeni

R3: k=3; 5 termeni

……………………………………….

R200: k=200; 2•200-1=399 termeni

In total sunt:

1+3+5+7+…..+399=

=1+3+5+7+…..+2•200-1

=200²

=40000 (numere)