give the ternary expansion of 12Solutionternary expansion me

give the ternary expansion of 1/2

ternary expansion means ..exapansion by using base-3

we need negative powers of 3
Also, 1/3 < 1/2,

but 1/2 < 2/3

So the first digit behind the decimal is equal to 1

we will use 1*3^{-1}
now, we are left with (1/2 - 1/3) to write as a sum of the other digits

This is 1/6
But 1/9 (3^{-2}) < 1/6 < 2/9,

so we again use 1*3^{-2}

We are left with 1/6 - 1/9 = 3/18 - 2/18 = 1/18
we can continue with 3^{-3} and we

see if it fits 0,1 or 2 times below 1/18
We can see that we are getting 1\'s

so, we get

[1/3 + 1/3^2 + 1/3^3 + .. ]is a geometric series with
ratio= 1/3 and first term =1/3,

so the sum is:
1/3 / (1 - 1/3) [first term / (1 - ratio)] = 1/3 / 2/3 = 1/2...........Answer