Question

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

Short answer

Proved

Step-by-step solution

Step 1. Given

Consider the sequence ${{\left\{a_k\right\}}_{k=n}}^{\infty }$.

Step 2. Proof

$$\begin{gathered} \mathrm{As}\mathrm{the}\mathrm{given}\mathrm{sequence}{{\left\{{\mathrm{a}}_{\mathrm{k}}\right\}}_{\mathrm{k}=\mathrm{n}}}^{\infty }\mathrm{starts}\mathrm{from}\mathrm{n}\mathrm{to}\infty \\ \mathrm{Since}\mathrm{the}\mathrm{sequence}\mathrm{is}\mathrm{tending}\mathrm{to}\mathrm{infinity} \\ \mathrm{so}\mathrm{if}\mathrm{we}\mathrm{start}\mathrm{k}=1\mathrm{then}\mathrm{the}\mathrm{sequence}\mathrm{makes}\mathrm{no}\mathrm{difference} \\ Henceproved \\ {{\left\{a_k\right\}}_{k=n}}^{\infty }={{\left\{a_k\right\}}_{k=1}}^{\infty } \end{gathered}$$