x→0 lim(sinx/x+2sin2x/x+...+nsin nx/x)+limx²=14
lim x²=0
limsinx/x+2limsin2x/x+...+nlim sinnx/x=14
Tinem cont ca lim sinx/x=1 si lim sin kx/kx=1 x→0
lim sin2x/x=lim 2sin2x/2x=2lim sin2x/2x=2*1=2
........................................................................................
lim sin nx/x= limn*sinnx/nx=n*limsin nx/nx=n*1=n
Inlocuim in relatia de mai sus si obtinem
1+2*2+3*3+...+n*n=1+2²+3²+...+n²=n(n+1)*(2n+1)/6=14
n(n+1)(2n+1)=84
n=3
