Question: How do I prove this theorem using real analysis? Exercise 2.7.12 (Summation-by-parts). Let (In) and (Un ) be sequences, let Sn = X1+x2+ . .

How do I prove this theorem using real analysis?

Exercise 2.7.12 (Summation-by-parts). Let (In) and (Un ) be sequences, let Sn = X1+x2+ . . . +n and set so = 0. Use the observation that xj = Sj - Sj-1 to verify the formula n n E Xjyj = Snyn+1 - Sm-1ym + si (yj - yi+1 ). 1=m 1=m

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