Binomial Theorem And Its Simple Applications Question 212
Question: $ \sqrt{5}[{{(\sqrt{5}+1)}^{50}}-{{(\sqrt{5}-1)}^{50}}] $ is
Options:
A) An irrational number
B) 0
C) A natural number
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ \sqrt{5}[ {{( \sqrt{5}+1 )}^{50}}-{{( \sqrt{5}-1 )}^{50}} ] $
$ =2\sqrt{5}[ ^{50}C_1{{( \sqrt{5} )}^{49}}+{{,}^{50}}C_3{{( \sqrt{5} )}^{47}}+…. ] $
$ =2[ ^{50}C_1{{( \sqrt{5} )}^{50}}+{{,}^{50}}C_3{{( \sqrt{5} )}^{48}}+…. ] $ = a natural number
BETA
