2. (5pts) Below it is discussed how to simplify 1 kxk (x 1) with change of index

Question

2. (5pts) Below it is discussed how to simplify 1 kxk (x 1) with change of index. Fill in the five blanks with the shortest possible expressions to complete the sentences. Allowed keystroke: power A Put the sum in S. Consider the two sums in Tl km1 In the second sigma notation, change the index k into j-k+1. So we have k=1 Then re-write j back to k. Find that it is equal to 7L k=1 x-1 The sigma notation in the right hand side is z l as we remember in class Solve this for S to find the closed formula. (7pts) Fill in the five blanks to complete the argument below to approximate nl as a double inequality 3.

Explanation / Answer

The answer will be as the explanation is given in the question itself

a) x^(k+1)

b)

j=k+1=2

c)

j=n+1

d)

(j-1)x^j

e) nx^(n+1)

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