Răspuns:
ex.6.
1/1•3+1/3•5+1/5•7+.....+1/19•21=
m/2•m+1=>m/2•m+1=
2/5+1/7•(1/5+1/9)+1/11•(1/9+1/13)+
1/15•(1/13+1/17)+1/19•(1/17+1/21)
<=>m/2•m+1=2/5+2/45+2/117
+2/221+2/357<=>m/2•m+1
=2/9•(2+1/13)+2/17•(1/13+1/21)
<=>m/2•m+1=6/13+4/273
<=>m/2•m+1=10/20+1
<=>21•m=20•m+10=>m=10
Așa se rezolvă acest exercițiu,prin calcul folosind factorul comun.
