lim x → ∞ 3 x + 1 + 3 x - 1 6 + 3 x + 1 - 3 x - 1 6 x + x 2 - 1 6 + x - x 2 - 1 6 x 3

Step-by-step solution

lim   x 3 x → ∞ 3 x + 1 + 3 x - 1 6 + 3 x + 1 - 3 x - 1 6 x + x 2 - 1 6 + x - x 2 - 1 6 We know the binomial expansion of a + b n and a - b n is given by, a + b n = C 0 n a n b 0 + C 1 n a n - 1 b 1 + C 2 n a n - 2 b 2 + . . . . . . + C n n a 0 b n a - b n = C 0 n a n b 0 - C 1 n a n - 1 b 1 + C 2 n a n - 2 b 2 - . . . . . . + C n n a 0 b n So, a + b 6 + a - b 6 = 2 T 1 + T 3 + T 5 + T 7 = 2 C 0 6 a 6 + C 2 6 a 4 b 2 + c 4 6 a 2 b 4 + C 6 6 b 6 From equation (1) we get, lim   x 3 x → &#8