Understanding the prove of sequence's sum rule

[garyljc]

the theorem is as stated that
1. suppose a(n) tends to a and b(n) tends to b , where a and b are constants
prove that a(n) + b(n) tends to a+b

what approach should i use ?
i was thinking about the definition of null sequences

 

[EnumaElish]

What is your definition of "tends to"?

 

[garyljc]

what do you mean what's my definition ?
tends to = eventually ?

 

[HallsofIvy]

Which would lead to the question "what is the definition of 'eventually'". I doubt that it is the usual one. The sequence {1/n}, I would say, "tends to 0" but is NEVER equal to 0. Does it make sense to say it is "eventually" 0?

I also doubt you will ever see a definition in a book like that! What is the definition in your textbook- not some general idea of what it means. In proofs you use the specific words of definitions. Being precise is extremely important.

You are told that an "tends to a" (which, I hope, means the limit of the sequence {an} is a). What does that tell you? What inequality does that give you?