series numériques telescópiques

∑ ( 1/(n(n+1)) ) = ∑ ( ( 1/n )+(-1)( 1/(n+1) ) ) < 1


∑ ( m/(n(n+m)) ) = ∑ ( ( 1/n )+(-1)( 1/(n+m) ) ) < 1+(1/2)+...+(1/m)


∑ ( 1/(n(n+m)) ) < (1/m)·( 1+(1/2)+...+(1/m) )


∑ ( 2/(n(n+2)) ) = ∑ ( ( 1/n )+(-1)( 1/(n+2) ) ) < (3/2)
∑ ( 3/(n(n+3)) ) = ∑ ( ( 1/n )+(-1)( 1/(n+3) ) ) < (11/6)


∑ ( 1/(n(n+2)) ) < (3/4)
∑ ( 1/(n(n+3)) ) < (11/18)