Limit of Sigma Notation

[lev888]

1)[MATH]\sum_{k=1}^n1 [/MATH] You start at 1 and then add to infinity by 1. [1+2+3+4...n] Which will be infinity see there is no upper bound.

Is this what I'm doing in Lev888's problem? Since there is no upper bound, the expression just goes to positive infinity?

First, [MATH]\sum_{k=1}^nk [/MATH], not [MATH]\sum_{k=1}^n1 [/MATH].
Second, 1+2+3+4...n is correct.
Third, what infinity? k iterates from 1 to n, where are you getting infinity?

 

[Steven G]

1)[MATH]\sum_{k=1}^n1 [/MATH] You start at 1 and then add to infinity by 1. [1+2+3+4...n] Which will be infinity see there is no upper bound.

Not [1+2+3+4...n] but rather [1+2+3+4+...+n]
If we wanted to write 1 + 2 + 3 forever we would write 1+2 + 3 + 4 + ....
Note that there is NOTHING after the three dots. If you had something after the three dots then continue the pattern up to the last number listed.
EX: 1 + 2 + 3 + ... + 19 + 20 means to add the 1st 20 positive integers.