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Some Funny Mathematical Questions
Fun With Math Interesting Math Problems 1. Which one is larger in between \(50^{50}\) and \(49^{51}\) ? Ans: \( \frac{50^{50}}{49^{51}}=\frac{50^{50}}{49^{50}\times49}=\frac{(49+1)^{50}}{49^{50}\times 49}=\left(\frac{49+1}{49}\right)^{50} \times \frac{1}{49}= \left(1 +\frac{1}{49}\right)^{50} \times \frac{1}{49}< e \times \frac{1}{49} \) \(=\left(1 +\frac{1}{49}\right)^{49}\times \left(1 +\frac{1}{49}\right) \times \frac{1}{49}< e \times\left(1 +\frac{1}{49}\right)\times \frac{1}{49} [As \lim_{x\to \infty}\left( 1+ \frac{1}{x}\right)^x = e]\) \(< e \times\frac{50}{49}\times \frac{1}{49}=2.703 \times\frac{50}{49}\times \frac{1}{49}\) \( \frac{135}{2401} < 1 \Rightarrow 50^{50} < 49^{51} \) 2
