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(1.003)^{4} is nearly equals to

  • Option 1)

    1.012

  • Option 2)

    1.0012

  • Option 3)

    0.988

  • Option 4)

    1.003

 

Answers (1)

As learnt in concept

Binomial Theorem for Rational index -

\left ( 1+x \right )^{n}= 1+nx+\frac{n\left ( n-1 \right )x^{2}}{2!}+\frac{n\left ( n-1 \right )\left ( n-2 \right )x^{3}}{3!}+-----
 

- wherein

use ^{n}c_{r}= \frac{n!}{r!(n-r)!}

n> 0

 

 If x<<<1, then we approximate

(1+x)^{n}\cong 1+nx

(1.003)^{4}= (1+0.003)^{4}\cong 1+4*0.003

\cong 1+0.012 \cong 1.012

 


Option 1)

1.012

Correct option

Option 2)

1.0012

Incorrect option

Option 3)

0.988

Incorrect option

Option 4)

1.003

Incorrect option

Posted by

Vakul

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