Using binomial theorem, indicate which is larger (1.1)10000 or 10… - Vidyadip

Question

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

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Answer

We have,

$(1.1)^{10000}=(1+0.1)^{10000}$

$={^{10000}\text{C}}_0+{^{10000}\text{C}}_1(0.1)+{^{10000}\text{C}}_2(0.1)^2+...+{^{10000}\text{C}}_{10000}(0.1)^{10000}$

= 1 + 10000 × (0.1) + other positive terms

= 1 + 1000 + other positive terms

= 1001 + other positive terms > 1000

$\therefore$ (1.1)¹⁰⁰⁰⁰> 1000

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