Question

Rpede ex de jos ultimul unde scrie S addica suma gaus egal cu ??

Answer 1

S = 3 + 33 + 333 + ....  +3....333 (de 2015 ori)
S = 3 (1 + 11 + 111 + .... +111....1111 (de 2015 ori) ) 
S = 3 [(1) + (1+10) + (1+10+100) + ... + (1+10+100+...+10^2014) 
S = 3 [(10−1)/(10−1) + (10^2−1)/(10−1) + (10^3−1)/(10−1) + ... + (10^2015−1)/(10−1)] 
S = 3/9 [(10 + 10^2 + 10^3+ ... + 10^2015) − 2015] 
S = 1/3 [10 (10^2015−1)/(10−1) − 2015] 
S = 1/3 [10 (10^2015−1)/9 −2015]
S=(10^2016-10)/27-2015/3
S= 999...990 (9 de 2015 ori)/27-2015/3
s=111....110 (1 de 2015 ori)/3-2015/3