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
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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
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