Asked by HELP
                Determine whether each of the following is always, sometimes, or never true. If the answer is sometimes true, state the conditions under which it would be true.
sn+1 - sn = an+1
            
        sn+1 - sn = an+1
Answers
                    Answered by
            oobleck
            
    is the n and n+1 a subscript?
If so, then we appear to be talking about the sequence of partial sums of a sequence.
So, take a look...
sn = a1 + a1 + ... + an
s_n+1 = a1 + a2 + ... + a_n + a_n+1
clearly, s_n+1 = s_n + a_n+1
so, s_n+1 - s_n = a_n+1 always
    
If so, then we appear to be talking about the sequence of partial sums of a sequence.
So, take a look...
sn = a1 + a1 + ... + an
s_n+1 = a1 + a2 + ... + a_n + a_n+1
clearly, s_n+1 = s_n + a_n+1
so, s_n+1 - s_n = a_n+1 always
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