Write the series with Sigma Notation. 1+(-1/4)+1/9+(-1/16)+...+1/576

Question

I know that the upper bound= 1/576 and the lower bound=1 but I am struggling to write the expression part because I can't find a common ratio or common difference.

Answer 1

1) The signs change for each term in the series. That means you need a factor of -1 raised to some power to alternate the signs of each term.

2) Just looking at the denominators in each element, each value is a square (power of 2) of a series of integers: 1 is 1², 4 is 2², 9 is 3², and so on. Therefore the denominators are n² for n = 1 to 24 (24² = 576).

3) Now let's put this together in Sigma Notation:

Some additional notes:

1) The first term is positive, therefore the (-1) term must have an even value of exponent for the first term. Since n starts at 1, n-1 is needed to make sure the first value is even (in this case zero).

2) In your problem statement, you have the last term 1/576 being positive. That does not correspond to each term alternating signs. Please check your problem statement.