Question

S
a se arate ca numarul S=1+2+2la2+2la3+2la4+2la5+...........2la1997 se divide cu 7
Repede va roggggggggggggggggggggg!!!!!!!!!!!!!!!!!

Answer 1

S=1+2+4+2^3 (1+2+4) + 2^6 (1+2+4) +...+ 2^1995 (1+2+4) =
= (1+2+4)(1+2^3 + 2^6 +...+ 2^1995)=
=7(...................................) = multiplu de 7, deci se divide cu 7.
Succes!!!