Correct Answer - Option 2 : 7
Given:
\(\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots up\;to\;\infty } } } } \)
Concept used:
Convergence and divergence of the infinite product
Calculations:
\(\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots \infty } } } } \) = x ----(1)
Squaring both sides
\(7\sqrt {7\sqrt {7\sqrt {7\sqrt {7 \ldots \ldots\infty } } } } \) = x2
⇒ x2 = 7x ----(From eq (1))
Hence, x = 7
∴ The value of the given expression is 7
