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sammy [17]
2 years ago
9

Using induction, verify the inequality. (1 + x)" ? 1 + nx, for x ?-1 and ? 1

Mathematics
1 answer:
klio [65]2 years ago
3 0

Answer with explanation:

The Inequality should be:

   (1+x)^n\geq 1+n x

Where, n and x are any integers.

⇒For, x= -1

L HS

 =[1+(-1)]^n\\\\=(0)^n\\\\=0

R HS

→1+n × (-1)

=1-n

If, n is any Integer, then for, n=1

1-1=0

For, n=2

1-2= -1

....

So,   (1+x)^n\geq 1+n x

for, x=-1.

⇒For, x=1

L HS

 =[1+(1)]^n\\\\=(2)^n

For, n=1

L H S=1

For, =2

L H S=4

R HS

→1+n × (1)

=1+n

If, n is any Integer, then for, n=1

1+1=2

For, n=2

1+2= 3

....

So,    (1+x)^n\geq 1+n x

for, x=1.

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