Given that the coefficient of the third term in the expansion of (1+3x)^n, in ascending powers of x, is 1539, find the value of n where n is a positive integer

n = 19

Step-by-step explanation:

Third term coefficient:

nCr = n!/((n - r)!r!)

nC2 = 171

n!/((n - 2)!2!) = 171

n!/2(n - 2)! = 171

n!/(n - 2)! = 342

n.(n - 1).(n -2).../((n - 2).(n - 3).(n - 4)...) = 342

n(n - 1) = 342

n² - n = 342

(n - ½)² - ¼ = 342

(n - ½)² = 1369/4

(n - ½) = ±37/2

n = 1/2 ± 37/2

n = -18 or n = 19

Since we are told n is a positive integer, it is 19

range is infinite on both x and y axis positive and negative

step-by-step explanation:

b

step-by-step explanation: