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  • Help me understand! - Binomial theorem and its simple applications - JEE Main-2

The positive integer just greater than  (1+.0001)^{10000}  is

  • Option 1)

    4

  • Option 2)

    5

  • Option 3)

    2

  • Option 4)

    3

 

Answers (1)

best_answer

As we have learned

Expression of Binomial Theorem -

\left ( x+a \right )^{n}= ^{n}\! c_{0}x^{n}a^{0}+^{n}c_{1}x^{n-1}a^{1}+^{n}c_{2}x^{n-2}a^{2}x-----^{n}c_{n}x^{0}a^{n}

 

- wherein

for n  +ve integral .

 

 S= (1+ \frac{1}{1000})^{1000} = ^{10000}C_0+ ^{10000}C_1\frac{1}{1000}+ ^{10000}C_2\frac{1}{1000}^2 +...+ ^{10000}C_{10000}\frac{1}{1000}^{10000}

1+1+ \frac{ ^{10000}C_2}{(10000)^2}+ ......+ \frac{ ^{10000}C_{10000}}{(10000)^{10000}}

 

 

1+1+ \frac{(10000)(9999)}{(10000)^2(2)!}+ \frac{(10000)(9999)(9998)}{(10000)^3 (3)!}+......\\< 1+1+ \frac{1}{2!}+\frac{1}{3!}+....+\frac{1}{(10000)!}

< 1+\frac{1}{1!}+ \frac{1}{2!}+ ... \infty = e^({ \frac{1}{10000}})!

So 2 < S c e 

 

 

 

 


Option 1)

4

Option 2)

5

Option 3)

2

Option 4)

3

Posted by

gaurav

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