83. Prove part (i) of Theorem 8 .

To prove: The series ∑n=1∞can=c∑n=1∞an .

Proof:

The series ∑n=1∞can is written as follows,

limn→∞∑i=1ncai=limn→∞c∑i=1nai=climn→∞∑i=1nai=c∑n=1∞an

That is, ∑n=1∞can=c∑n=1∞an .

Hence, the required result.