Math, asked by tarangkamble6730, 9 months ago

If the sum of the coefficients in (1+x)^n is 512 than what is the value of n?

Answers

Answered by DevendraLal
0

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.

Answered by amitnrw
0

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

Learn more:

The first three terms in the binomial expansion of ( ) n x y + are 1, 56 ...

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