Cho dãy số (un) xác định bởi u1=1 và un+1=(un+2)/(un+1)

Ta có

u2=u1+2u1+1=1+21+1=32;               u3=u2+2u2+1=32+232+1=75;         u4=u3+2u3+1=75+275+1=1712;             u5=u4+2u4+1=1712+21712+1=4129;         u6=u5+2u5+1=4129+24129+1=9970;             u7=u6+2u6+1=9970+29970+1=239169;Vậy u8=u7+2u7+1=239169+2239169+1=577408;