Fill in the numbers 1,3,2,6,4 (), (), 12, ()

Fill in the numbers 1,3,2,6,4 (), (), 12, ()


1 3 2 6 4 (9) (8) 12 (16)
Look at the first number, the third number, the fifth number: 1, 2, 4, the seventh number is 8, and the ninth number is 16
Let's look at the second, the fourth and the eighth: 3, 6 and 12, so the sixth number is 9,



√ 2 / 3 - (1 / 6 √ 24-3 / 2 √ 12) equals
First simplify √ 2 / 3 - (1 / 6 √ 24-3 / 2 √ 12), and then find its approximate value as (). (accurate to 0.01, √ 2 ≈ 1.414, √ 3 ≈ 1.732)


√2/3-(1/6√24-3/2√12)
=√2/3-(√6/3-3√3)
=√2/3-(√2/3-3√3)
=3√3
=5.20
(2 / 3 of the first item above are in the root)
√2/3-(1/6√24-3/2√12)
=√2/3-√6/3+3√3
=(√2(1-√3)+3√3)/3
=1.39
(the first item above, 3 is outside the root)



1-2/3-1/6-1/12-1/24-1/48-…… 1/768


1-2/3-1/6-1/12-1/24-1/48-…… 1/768
=1/3-1/6-1/12-1/24-1/48-…… 1/768
=1/6-1/12-1/24-1/48-…… 1/768
=1/12-1/24-1/48-…… 1/768
=1/24-1/48-…… 1/768
=1/768