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Whats your question?

What does the sign inverted u mean

product of terms

ive seen this before :O

its like \(\sum \),
\[\large \prod_{k=1}^{3}k= (1)(2)(3)\]

\[\large \prod_{k=1}^{3}k^2= (1^2)(2^2)(3^2)\]

etc..

oh

the proof for the original question is simple

Yes then it is easy after i understood what the sign means

i will be back after dinner

mmm sure its a proof ?

so \(0@ganeshie8 ?

wait it can be rational but not integer

forget about the interval

\[(1+a _{1})(1+a _{2})(1+a _{3})(1+a _{4}) \cdots (1+a _{n}) = \prod \limits_{i=1}^{n} (a_i + 1)\]

right ?

yep

ahh i see your point, so we're given that \(a_i \gt 0\),
we're NOT given that its a natural number

okay then it cannot be an one liner >.<

lets expand the product

I got it how to do

only this case work , if \(1\le a_i \)
(1+3/2) (1+5/4) (1+7/6) >=2^3

nope we cant , we only can conclude that \(a_i\) is rational

for example
\(\dfrac{1}{2}×\dfrac{2}{3}×\dfrac{3}{1}×\dfrac{1}{1}=1\)

ok

gtg nw ,
have a nice day

nice :) AM/GM inequality to the rescue !!

yes, just didn't knew what that sign meant

cool O.O
never seen this before

AM-GM inequality : \(\dfrac{a+b}{2} \ge \sqrt{ab}\)

ic .. i dont think that ive seen it before :D