11 false 2 true equality needed in 1
Statement 1:- c2c3c4........cn < ( nn 2(n - 1)(n - 2) ) / (n!)2 cr = ncr
Because
Statement 2 :- For positive quantities AM ≥ GM.
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10 Answers
11Sorry both the statements are true......
I found out my mistake and got the answer.....
11[(1.2)c2 + (2.3)c3 + ..... + (n-1)n.cn] > [(n!)2c2c3......cn ]1/(n-1)
Now n Σ(r=2 to n) [r(r-1)ncr] / n(n-1) = n Σ(r=2 to n) n-2cr-2 = n2n-2
→ [n2n-2]n-1 > (n!)2c2c3......cn
→ c2c3......cn <[ nn-1 2(n-1)(n-2) n ]/ (n!)2
→ c2c3......cn < [nn2(n-1)(n-2) ] / (n!)2
62equality holds when all terms are equal.
think when will the equality hold?
62basically the equality will never hold because all terms will never be equal...
because nc2 ≠nc3 unless n=4.. but then they will not be equal to nc4!
wejust have to check for one case
n=2
where itis equal... !!!