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Chapter 7: Q. 92 (page 593)

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

Short Answer

Expert verified

Proved

Step by step solution

Step 1. Given

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

Step 2. Proof

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

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Most popular questions from this chapter

Given that $a_{0} = - 3, a_{1} = 5, a_{2} = - 4, a_{3} = 2$ and ${\sum a_{k}}_{k = 2}^{\infty} = 7$ , find the value ofrole="math" localid="1648828803227" ${\sum a_{k}}_{k = 3}^{\infty}$ .

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

Short Answer

Step by step solution

Step 1. Given

Step 2. Proof

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