series

Question 1

Describe the alternating series estimation theorem

Answer 1

If you stop at a certain term in an alternating series with decreasing magnitude, the error is less than the magnitude of the next omitted term.
i.e. first 4 terms < function < first 3 terms

assuming that the first term is positive

Question 2

What is the sum to infinity of a geometric series

Answer 2

S = a / (1-r)

Question 3

What is the sum to n of a geometric series

Answer 3

S = a(1 - r^n) / (1 - r)

Question 4

what is the sum to n of an arithmetic series

Answer 4

S = n/2 * (2a + (n-1)d)
which is equivalent to
S = n/2 (a + l)

where a is first term and l is the final (nth) term