Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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Using Binomial Theorem, Indicate Which is Larger (1.1)10000 Or 1000. - Mathematics

Using binomial theorem, indicate which is larger (1.1)10000 or 1000.

 
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Solution

We have:    
(1.1)10000

\[= (1 + 0 . 1 )^{10000} \]

\[ =^{10000}{}{C}_0 \times \left( 0 . 1 \right)^0 + ^{10000}{}{C}_1 \times (0 . 1 )^1 +^{10000}{}{C}_2 \times (0 . 1 )^2 + . . . ^{10000}{}{C}_{10000} \times (0 . 1 )^{10000} \]

\[ = 1 + 10000 \times 0 . 1 + \text{ other positive terms } \]

\[ = 1 + 10000 + \text{ other positive terms } \]

\[ = 10001 + \text{ other positive terms } \]

\[ \because 10001 > 1000\]

\[ \therefore (1 . 1 )^{10000} > 1000\]

Concept: Proof of Binomial Therom by Combination
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.1 | Q 9 | Page 12
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