Math, asked by bhau879, 11 months ago

If it is given that binomial coefficients of 2nd, 3rd and 4th term in expansion of (a + b)” are in A.P. and
the value of 3rd term is 84 (a, b = (1, 0)), then the maximum value of (log, 2B2) is equal
to​

Answers

Answered by amitnrw
1

Answer:

n = 7

Step-by-step explanation:

(a + b)ⁿ = aⁿ  + ⁿC₁aⁿ⁻¹b  + ⁿC₂aⁿ⁻²b² + ⁿC₃aⁿ⁻³b³  +.......

2nd Term = ⁿC₁

3rd Term = ⁿC₂

4th Term = ⁿC₃

ⁿC₁ + ⁿC₃ = 2 * ⁿC₂

n  + n(n-1)(n-2)/6  =  2*  n(n-1)/2

=> 1 + (n-1)(n-2)/6 = n-1

=> 6 + (n-1)(n-2) = 6n - 6

=> 6 + n² - 3n + 2 = 6n - 6

=> n² -9n + 14 = 0

=> n² - 2n - 7n + 14 = 0

=> (n-2)(n-7) = 0

=> n = 7   n can not be 2 as it will have 3 terms only

3rd term = ⁷C₂a⁵b² = 84

=> 21 * a⁵b² = 84

=> a⁵b² = 4

a = 1  b= ±2

Similar questions