1. Tardigrade
  2. Question
  3. Mathematics
  4. Let a=1 ⋅ 2 ⋅ 3 ⋅ 4 ⋅ 5. Then

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Q. Let $a=1 \cdot 2 \cdot 3 \cdot 4 \cdot 5$. Then

Sequences and Series

Solution:

Since $A.M. >G.M. $
$\Rightarrow \frac{1+2+3+4+5}{5} \geq \sqrt[5]{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5} $
$\Rightarrow 3 \geq \sqrt[5]{a} $
$\Rightarrow 3^{5} \geq a=5 !$
Also, $5^{5} \geq 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5=a$.