Răspuns :
e cam de liceu
se "observa " ca termenul general poate fi scris;
3/((n*(n+3))= 3* (1/3)*((1/n-1/(n+3))
3/(2*5)= 3* (1/3)(1/2-1/5)
3/(5*8)=3*(1/3)*(1/5-1/8)
3/(8*11)=3*(1/3)*(1/8-1/11)
................................................
3/(2012*2015)=3*(1/3)* (1/2012-1/2015)
adunand tot
ne da
1*(1/2-1/2015)=(2015-2)/ (2*2015)=2013/4030
se "observa " ca termenul general poate fi scris;
3/((n*(n+3))= 3* (1/3)*((1/n-1/(n+3))
3/(2*5)= 3* (1/3)(1/2-1/5)
3/(5*8)=3*(1/3)*(1/5-1/8)
3/(8*11)=3*(1/3)*(1/8-1/11)
................................................
3/(2012*2015)=3*(1/3)* (1/2012-1/2015)
adunand tot
ne da
1*(1/2-1/2015)=(2015-2)/ (2*2015)=2013/4030
3/2x5=1/2 - 1/5
3/5x8=1/5 - 1/8
3/8x11=1/8-1/11
........................
3/2009x2012=1/2009 - 1/2012
3/2012x2015=1/2012 - 1/2015 le adunam membru cu membru
S=1/2 - 1/2015=2013/4030
3/5x8=1/5 - 1/8
3/8x11=1/8-1/11
........................
3/2009x2012=1/2009 - 1/2012
3/2012x2015=1/2012 - 1/2015 le adunam membru cu membru
S=1/2 - 1/2015=2013/4030