Verified Solution • 2025–26 Session moderate

QJEEM21Mad4ee: JEE Main 2021 Mathematics - Class 11 JEEM21Mad4ee Solution

The value of 4+15+14+15+14+......∞4 + {1 \over {5 + {1 \over {4 + {1 \over {5 + {1 \over {4 + ......\infty }}}}}}}} is :

Multiple Choice Options

  • A 2 + 2530{2 \over 5}\sqrt {30}
  • B 2 + 4530{4 \over {\sqrt 5 }}\sqrt {30}
  • C 5 + 2530{2 \over 5}\sqrt {30}
  • D 4 + 4530{4 \over {\sqrt 5 }}\sqrt {30}

Step-by-Step Verified Solution

y=4+15+1yy = 4 + {1 \over {5 + {1 \over y}}}

⇒y=4+y5y+1\Rightarrow y = 4 + {y \over {5y + 1}}

⇒5y2−20y−4=0\Rightarrow 5{y^2} - 20y - 4 = 0

⇒y=20±400+8010\Rightarrow y = {{20 \pm \sqrt {400 + 80} } \over {10}}

\Rightarrow y = {{20 \pm 4\sqrt {30} } \over {10}},y > 0

∴\therefore y=10+2305y = {{10 + 2\sqrt {30} } \over 5}

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