Question

aratati ca numarul :
n=(3/2+4/3+5/4+...+1008/1007) : [2012-(1/2+2/3+3/4+...+1006/1007)] este numar natural

Answer 1

n= [ (2+1)/2 + (3+1)/3 + (4+1)/4+... + (1007+1)/1007] :
[2012 - ( (2-1)/2+(3-1)/3+(4-1)/4+..+ (1007-1)/1007 ) ]

n= [ 2/2+1/2+3/3+1/3+4/4+1/4+...+1007/1007 + 1/1007] :
[2012 - ( 2/2-1/2 +3/3-1/3 +4/4-1/4 + ....+1007/1007 - 1/1007]

n= [ 1+1/2+1+1/3+1+1/4+...+1 + 1/1007]:
[2012 - ( 1-1/2+1-1/3+1-1/4 + ...+ 1-1/1007]

n= ( 1006 + 1/2+1/3+1/4+...+1/1007) :
[ 2012 - (1006 -1/2-1/3-1/4-..-1/1007)]

n = ( 1006 + 1/2+1/3+1/4+...+1/1007) : (2012-1006 + 1/2+1/3+...+1/1007)

n=( 1006 + 1/2+1/3+1/4+...+1/1007) : ( 1006 + 1/2+1/3+1/4+...+1/1007)

n=1 ∈ N