Question

【急需解答】关于数列求通项的问题.

Answer 1

An=Sn-Sn-1=Sn×Sn-1

两边除以Sn×Sn-1得

1/Sn-1 － 1/Sn = 1

1/Sn-2 － 1/Sn-1 = 1

1/Sn-3 － 1/Sn-2 = 1

.

1/S1 － 1/S2 = 1

以上各式相加得

1/S1 － 1/Sn = n-1

1/Sn = 1/S1 － n + 1 = ·1/ a1 - n + 1 = 11/2 － n

Sn = 2/11-2n

an = Sn － Sn-1 = Sn × Sn-1 = 4/(11-2n)(13-2n), n≥2

a10= 4/(-9)(-7) = 4/63