If the sum of the coefficients in (1+x)^n is 512 than what is the value of n?
Answers
The value of n is 9.
In the given expression (1+x)^n, if we expand this using binomial theorem,
the coefficients will be nC0, nC1, nC2, till nCn.
So their summation is given as 2^n which is given to us as 512.
Therefore 2^n=512
n=9.
Value of n = 9 If the sum of the coefficients in (1+x)^n is 512
Step-by-step explanation:
(1 + x )ⁿ = ⁿC₀ 1ⁿx⁰ + ⁿC₁ 1ⁿ⁻¹x¹ + .....................................+ ⁿCₙ₋₁1¹xⁿ⁻¹ + ⁿCₙ1⁰xⁿ
=> (1 + x )ⁿ = ⁿC₀ x⁰ + ⁿC₁ x¹ + .....................................+ ⁿCₙ₋₁xⁿ⁻¹ + ⁿCₙxⁿ
Sum of coefficient = ⁿC₀ + ⁿC₁ + .....................................+ ⁿCₙ₋₁ + ⁿCₙ
=> ⁿC₀ + ⁿC₁ + .....................................+ ⁿCₙ₋₁ + ⁿCₙ = 512
(1 + x )ⁿ = ⁿC₀ x⁰ + ⁿC₁ x¹ + .....................................+ ⁿCₙ₋₁xⁿ⁻¹ + ⁿCₙxⁿ
putting x = 1
=> (1 + 1)ⁿ = ⁿC₀ 1⁰ + ⁿC₁1¹ + .....................................+ ⁿCₙ₋₁1ⁿ⁻¹ + ⁿCₙ1ⁿ
=> 2ⁿ = ⁿC₀ + ⁿC₁ + .....................................+ ⁿCₙ₋₁ + ⁿCₙ
=> 2ⁿ = 512
=> 2ⁿ = 2⁹
=> n = 9
Value of n = 9
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