Question

For x << 1, then value of (1 + x)nis
(A) 1 - nx
(B) 1/2(1- nx
)
(C) 1 + nx
(D) 1/2(1+ nx)​

Answer 1

Explanation:-

Binomial expansion is used here

And

As x << 1

So, x², x³, and all higher powers of x can be neglected

As, Let us suppose x = 0.01 which is (<< 1)

So, x² = 0.0001 and x³ = 0.000001 which are the values tending to 0

Hence, they are neglected

Hope u understood the solution

Pls mark me as brainliest.

Answer 2

Step-by-step explanation:

C

For all n>1, provided x



=0.

p(1) :(1+x)

1

> 1 + x is false

p(2) :(1+x)

2

>1+2x⇒x

2

> 0 is true when x



=0

p(3) :(1+x)

3

>1+3x⇒x

2

> 0 is true whenx



=0

Let p(k) (1+x)

k

> 1 + k x is true for some kϵN, k >1

⇒(1+x)

k+1

>(1+kx) (1+x)

⇒(1+x)

k+1

>1+(k+1)x+kx

2