1) provethat:(adsbygoogle = window.adsbygoogle || []).push({});

n n

sum(a_k)+1<= product(1+a_k)

k=1 k=1

when a_k>0 for every k natural, or when -1<a_k<0

2) x1,...x_n>0

n>1 x1x2..x_n=1

prove by induction on n that x1+x2+...+x_n>n

concerning the first question i tried to open the product this way:

n

product(1+a_k)=(1+a1)(1+a2)...(1+an)=1+a1(a2+..an)+a1a2...an+a2(a3+...+an)+a3(a4+...an)+an

from here its apparent that it's greater than the sum, is my opening correct?

about the second question:

i have these two:

x1+x2+...xn>k

k-1+x1+x2+..+xn>2k-1>=k+1

then i only need to prove that:

x1+..+xk+1>k-1+x1+...+xk

or:

xk+1>k-1

if we use this: x1x2...xkxk+1=xk+1

we get:

x1x2...xkxk+1>k-1

now how do i approach it from there on?

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# Homework Help: Two inequality questions.

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