Question

一道高一数学题求解要过程

Answer 1

追答

可好(✪▽✪)……😳😳😳

Answer 2

a_(n+1) = 4an/(an + 4)
=[4(an + 4)-16]/(an + 4)
=4 - 16/(an + 4)

a2=4-16/(2+4) = 4-8/3=4/3

a1a2=8/3

a3=4-16/(a2 + 4)=1

a4=4-16/(a3 + 4)=4-16/5 = 4/5

a5=4-16/(a4 + 4)=4-16*5/24 = 4-10/3 = 2/3 =4/6

a6=4-16/(a5 + 4)=4-16*3/14 = 4-24/7 = 4/7

a7=4-16/(a6 + 4)=4-16*7/32 = 4-7/2 = 1/2 =4/8

a8=4-16/(a7+ 4)=4-16*2/9 = 4/9

a9=4-16/(a8+ 4)=4-16*9/40 = 4-18/5=2/5 =4/10

a10=4-16/(a9+ 4)=4-16*5/22 = 4-40/11=4/11

a11=4-16/(a10+ 4)=4-16*11/48 = 4-11/3=1/3 =4/12

a12=4-16/(a11+ 4)=4-16*3/13 = 4-48/13=4/13

可以发现规律
an=4/(n+1)

令a1a2=8/3=4/x
则x=3/2，不是整数，因此不可能是数列中的项。