Question

Va rog sa ma ajutati.Intr-o ora am test la mate si nu am inteles aceasta problema:
2+2.2+2.22+2.222+...+2.222(9 ori)
Multumesc anticipat pt ajutor.

Answer 1

S = 2(1+2+22+222+.....+22......2)    S1 = S-2= 2(2+22+222+......+22.....2) S2=2+22+222+......+22.......2
2 = 2
22 = 2(1+10)
222= 2(1+10+10²)
2222 =2(1+10+10² +10³)
22222 = 2(1+10+10² +10³ +10^4)
.....................................................
222222222= 2(1+10+10² +10³ +......+10^8)
S2 = 2(1·9 +10·8 +10² ·7 + 10³ ·6 +10^4 ·5 + 10^5 ·4 + 10^6 ·3 + 10^7·2 +10^8 ·1) S2 =2·123456789
S1 = 2S2 = S-2 ⇒ S = 2S2 +2 = 4·123456789 +2 = 493827158