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