Răspuns:
2. a) (-1)^1 + (-1)^2 + (-1)^3 + ... + (-1)^2006 =
= -1 + 1 - 1 + 1 - ... -1 + 1 =
{de 1003 ori}
= 0
b) 1 + 3 - 2 - 4 + 3 + 5 - 4 - 6 + 5 + 7 - 6 - 8 + ... + 2003 + 2005 - 2004 - 2006 =
= -2 - 2 - 2 - ... - 2 =
{2006:2 - 1 = 1002 ori}
= -2*1002 =
= -2004
c) S = 5 + 9 + 13 + ... + 85 =
= 5 + 5+4 + 5+8 + ... + 5+80
Ca sa aflam cati cinci sunt :
85 - 4(x-1) = 5
4(x-1) = 80
x-1 = 20
x = 21
S = 5*21 + 4*(1 + 2 + 3 + ... + 20)
S = 5*21 + 4*20*21/2
S = 5*21 (1 + 8)
S = 105*9
S = 945
1. (n+6)/2 = (2n+4)/2 - 12
(2n+4)/2 - (n+6)/2 = 12
(2n+4-n-6)/2 = 12
n-2 = 24
n = 26
VERIFICARE :
(26+6)/2 = (52+4)/2 - 12
32/2 = 56/2 - 12
16 = 28 - 12
16 = 16 -> Adevarat :)
