Question

在數(shù)列{a_n}中,a₁=1,a_na_n-1=a_n-1+(-1)ⁿ(n≥2,n∈N^*),則的值是(　　)

A．

B．

C．

D．

Answer 1

C

當(dāng)n=2時,a₂·a₁=a₁+(-1)²,∴a₂=2.
當(dāng)n=3時,a₃a₂=a₂+(-1)³,∴a₃=.
當(dāng)n=4時,a₄a₃=a₃+(-1)⁴,∴a₄=3.
當(dāng)n=5時,a₅a₄=a₄+(-1)⁵,∴a₅=,∴=.