Question

已知数列{an}是一个公差不为零的等差数列且a2=2 a3 a6 a12成等比数列

Answer 1

a3
a6
a12成等比数列
a6*a6=a3*a12=(a6-3d)(a6+6d)
d=1
a2=2
a1=1
an=n
1/（a1*a3）+1/（a2*a4）+1/（a3*a5）+......+1/（an+an+2）
可用拆项求和.
原式=(1/2d)*(1/a1
-
1/a3
+
1/a2
-
1/a4
+
1/a3
-
1/a5
+..+
1/an
-
1/an+2
)
=(1/2)*(1/a1
+
1/a2
-
1/an+1
-
1/an+2)
=(1/2)*(3/2
-
1/n+1
-
1/n+2)
化简得：原式=(3n^2
+5n)/4(n+1)(n+2)

Answer 2

a3
a6
a12成等比数列
a6*a6=a3*a12=(a6-3d)(a6+6d)
d=1
a2=2
a1=1
an=n
1/(a1*a3)+1/(a2*a4)+1/(a3*a5)+......+1/(an+an+2)
可用拆项求和.
原式=(1/2d)*(1/a1
-
1/a3
+
1/a2
-
1/a4
+
1/a3
-
1/a5
+..+
1/an
-
1/an+2
)
=(1/2)*(1/a1
+
1/a2
-
1/an+1
-
1/an+2)
=(1/2)*(3/2
-
1/n+1
-
1/n+2)
化简得:原式=(3n^2
+5n)/4(n+1)(n+2)