Watch the difference
between coefficients of drag (or lift) and the actual values for drag and lift.
The coefficient of
induced drag is proportional to the square of the coeficient of lift.
This is because the more
lift you need the greater the downwash and all the other factors that generate
induced drag.
Now write angle of
attack in place of the coeficient of lift, and consider level flight.
In level flight, from
the lift formula, as you speed up alpha goes down, proportionally as the square
of increasing IAS. But the “coefficient” of induced drag is proportional to
alpha squared, and as alpha is decreasing as the square of IAS the coefficent
of induced drag is decreasing as the fourth power of IAS.
But the actual
induced drag is the coefficient times the square of increasing IAS, and this
now makes the actual induced drag decrease as the square of IAS
So with the IAS
doubling in level flight the coefficient of induced drag, Cdi, is down 1/16,
but the actual induced drag is down 1/4.