How to show the following is true?I need a proof of the following. If a 1 b 1 = a 2 b 2 = ⋯ = a K b K = Tthen a i b i = ∑ i = 1 K a i ∑ i = 1 K b k where all the a i 's and b i 's are positive values.

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How to show the following is true?I need a proof of the following. If            a      1              b      1        =            a      2              b      2        =  ⋯  =            a      K              b      K        =  Tthen            a      i              b      i        =                    ∑                  i          =          1                K                    a        i                            ∑                  i          =          1                K                    b        k            where all the       a    i  &#039;s and       b    i  &#039;s are positive values.

Kristin Myers · Accepted Answer

∑                  i          =          1                K                    a        i                            ∑                  i          =          1                K                    b        i              =                    ∑                  i          =          1                K            (      T              b        i            )                      ∑                  i          =          1                K                    b        i              =            T              ∑                  i          =          1                K                    b        i                            ∑                  i          =          1                K                    b        i              =  T  =            a      i              b      i        .

Kevin Charles · Accepted Answer

You have   ∑      a    i    =  T  ∑      b    i      ⟹                      a        i                    b        i              =  T  =                    ∑                  a          i                            ∑                  b          i

How to show the following is true? I need a proof of the following. If (a_1)/(b_1)=(a_2)/(b_2)=... =(a_K)/(b_K)=T then (a_i)/(b_i)=(sum_(i=1)^Ka_i)/(sum_(i=1)^Kb_k) where all the a_i's and b_i's are positive values.

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