(1)在和式1/2×4+1/4×6+1/6×8+.+1/38×40
第8项是1/16×18.1/24×26是第12项
(2)1/3×6+1/6×9+1/9×12+.+1/27×30
=(1/3)(1/3-1/6)+(1/3)(1/6-1/9)+(1/3)(1/9-1/12)+.+(1/3)(1/27-1/30)
=(1/3)(1/3-1/6+1/6-1/9+1/9-1/12+.+1/27-1/30)
=(1/3)(1/3-1/30)
=(1/3)(3/10)
=1/10
(3)1/√x(√x+4)+1/(√x+4)(√x+8)+.+1/(√x+16)(√x+20)=5/69
(1/4)[1/√x-1/(√x+4)+1/(√x+4)-1/(√x+8)+.+1/(√x+16)-1/(√x+20)]=5/69
(1/4)(1/√x-1/(√x+20)]=5/69
x-20√x+69=0
(√x-23)(√x+3)=0
√x=23,x=529
√x=-3(舍去)