Question

两道数列的题1.设正数a1,a2,a3……,an成等差数列,求证 1/（√a1+√a2）+1/（√a2+√a3）+……+

Answer 1

1.证明：分母有理化得：

左边=(根a1-根a2)/(a1-a2) +.+(根an-根an+1)/(an-an+1)

=-[(根a1-根a2)/d+.+（根an-根an+1)/d]

=-(根a1-根a2+根a2-根a3+.+根an-根an+1)/d

=-(根a1-根an+1)/d

再分子有理化：

=-（a1-an+1）/[d*(根a1+根an+1)

=-(-nd)/[d*(根a1+根an+1)

=n/(根a1+根an+1)=右边

所以原结论成立.

2.a1+a6+a16=a1+d+a1+5d+a1+15d

=3a1+21d

=3(a1+7d)

=3a8

所以3a8=m

所以a8=m/3,为确定的值

所以p=8