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Chapter 7: Q. 92 (page 593)

Prove that every sequence of the form ${\{a_{k}\}}_{k = n}^{鈭�}$ can be rewritten as a sequence of the form ${\{a_{k}\}}_{k = 1}^{鈭�}$ .

Short Answer

Expert verified

Proved

Step by step solution

Step 1. Given

Consider the sequence ${\{a_{k}\}}_{k = n}^{鈭�}$ .

Step 2. Proof

$As the given sequence {\{a_{k}\}}_{k = n}^{鈭�} starts from n to 鈭� Since the sequence is tending to infinity so if we start k = 1 then the sequence makes no difference H e n c e p r o v e d {\{a_{k}\}}_{k = n}^{鈭�} = {\{a_{k}\}}_{k = 1}^{鈭�}$

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Prove that every sequence of the form akk=n鈭�can be rewritten as a sequence of the form akk=1鈭�.

Short Answer

Step by step solution

Step 1. Given

Step 2. Proof

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Prove that every sequence of the form ${\{a_{k}\}}_{k = n}^{鈭�}$ can be rewritten as a sequence of the form ${\{a_{k}\}}_{k = 1}^{鈭�}$ .