Question

What is an alternating sequence?

Answer 1

See explanation

Explanation:

Alternating sequence is a sequence, whose term change sign (i.e. if a term `a_n` is positive then `a_{n+1}` is negative and vice versa)

Examples:

1. `a_n=(-1/2)^n`
   This sequence would have terms: `-1/2;1/4;-1/8;1/16;...`

2. `b_n=(-1)^n`.
   This sequence would have terms: `-1;1;-1;1;...`

3. `c_n=(-1)^n*n`
   This sequence would have terms: `-1;2;-3;4;...`

Note that such terms can be either convergent: `lim_{n->oo}a_n=0`, or divergent: `lim_{n->oo}b_n` does not exist