A) \[{{99}^{50}}+{{100}^{50}}\]
B) Both are equal
C) \[{{101}^{50}}\]
D) None of these
Correct Answer: C
Solution :
We have \[{{101}^{50}}={{(100+1)}^{50}}={{100}^{50}}+{{50.100}^{49}}+\frac{50.49}{2.1}{{100}^{48}}+....\] ?..(i) and\[{{99}^{50}}={{(100-1)}^{50}}={{100}^{50}}-{{50.100}^{49}}+\frac{50.\,49}{2.1}{{100}^{48}}-..\]?..(ii) Subtracting (ii) from (i), we get \[{{101}^{50}}-{{99}^{50}}={{100}^{50}}+2\frac{50.49.48}{1.2.3}{{100}^{47}}>{{100}^{50}}\] Hence 10150 > 10050+9950.
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