recurrence relation and sigma notation

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Can anyone help me and explain with sigma notation rules how does this equation solved



The problem for me that $T(i)$ and $T(i-1)$ are inside sigma notation(not i) so i am confused. Please anyone show me how is it calculated ?



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recurrence-relations




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    up vote
    -3
    down vote

    favorite












    Can anyone help me and explain with sigma notation rules how does this equation solved



    The problem for me that $T(i)$ and $T(i-1)$ are inside sigma notation(not i) so i am confused. Please anyone show me how is it calculated ?



    enter image description here




    recurrence-relations




    share|cite|improve this question























      up vote
      -3
      down vote

      favorite









      up vote
      -3
      down vote

      favorite











      Can anyone help me and explain with sigma notation rules how does this equation solved



      The problem for me that $T(i)$ and $T(i-1)$ are inside sigma notation(not i) so i am confused. Please anyone show me how is it calculated ?



      enter image description here




      recurrence-relations




      share|cite|improve this question













      Can anyone help me and explain with sigma notation rules how does this equation solved



      The problem for me that $T(i)$ and $T(i-1)$ are inside sigma notation(not i) so i am confused. Please anyone show me how is it calculated ?



      enter image description here





      recurrence-relations





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      edited 2 days ago









      pointguard0

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          $$
          forall ninmathbbN, n>1,T(n)=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
          forall n>2, T(n-1)=sumlimits_i=1^n-2(T(i)+T(i-1)+c)
          $$
          Now:
          $$
          beginalign
          T(n)&=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
          &=T(n-1)+T(n-2)+c+underbracesumlimits_i=1^n-2(T(i)+T(i-1)+c)_=T(n-1)\
          &=T(n-1)+T(n-2)+c+T(n-1)\
          &=2T(n-1)+T(n-2)+c
          endalign
          $$






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            $$
            forall ninmathbbN, n>1,T(n)=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
            forall n>2, T(n-1)=sumlimits_i=1^n-2(T(i)+T(i-1)+c)
            $$
            Now:
            $$
            beginalign
            T(n)&=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
            &=T(n-1)+T(n-2)+c+underbracesumlimits_i=1^n-2(T(i)+T(i-1)+c)_=T(n-1)\
            &=T(n-1)+T(n-2)+c+T(n-1)\
            &=2T(n-1)+T(n-2)+c
            endalign
            $$






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              $$
              forall ninmathbbN, n>1,T(n)=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
              forall n>2, T(n-1)=sumlimits_i=1^n-2(T(i)+T(i-1)+c)
              $$
              Now:
              $$
              beginalign
              T(n)&=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
              &=T(n-1)+T(n-2)+c+underbracesumlimits_i=1^n-2(T(i)+T(i-1)+c)_=T(n-1)\
              &=T(n-1)+T(n-2)+c+T(n-1)\
              &=2T(n-1)+T(n-2)+c
              endalign
              $$






              share|cite|improve this answer























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                $$
                forall ninmathbbN, n>1,T(n)=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
                forall n>2, T(n-1)=sumlimits_i=1^n-2(T(i)+T(i-1)+c)
                $$
                Now:
                $$
                beginalign
                T(n)&=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
                &=T(n-1)+T(n-2)+c+underbracesumlimits_i=1^n-2(T(i)+T(i-1)+c)_=T(n-1)\
                &=T(n-1)+T(n-2)+c+T(n-1)\
                &=2T(n-1)+T(n-2)+c
                endalign
                $$






                share|cite|improve this answer













                $$
                forall ninmathbbN, n>1,T(n)=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
                forall n>2, T(n-1)=sumlimits_i=1^n-2(T(i)+T(i-1)+c)
                $$
                Now:
                $$
                beginalign
                T(n)&=sumlimits_i=1^n-1(T(i)+T(i-1)+c)\
                &=T(n-1)+T(n-2)+c+underbracesumlimits_i=1^n-2(T(i)+T(i-1)+c)_=T(n-1)\
                &=T(n-1)+T(n-2)+c+T(n-1)\
                &=2T(n-1)+T(n-2)+c
                endalign
                $$







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered 2 days ago









                Quantic_Solver

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