Question

Write the sum −1 + 2−3+ 4−5+6−7 8−9 using sigma notation. the form of your answer will depend on your choice of the lower limit of summation.

Answer 1

The sum −1 + 2−3+ 4−5+6−7+8−9 can be expressed in sigma notation as ∑¹⁻¹(-1)^{i+1} ⋅ i for i = 1 up to 9, effectively alternating the sign of each subsequent term.

Step-by-step explanation:

The sequence given by the student is alternating between negative and positive terms beginning with a negative term, and the absolute value of the terms is increasing linearly (by 1 each time). The sum can be expressed in sigma notation as follows:

∑¹⁻¹(-1)^{i+1} ⋅ i for i = 1 up to 9.

This translates to summing over the index i, starting at 1 and going up to 9, the product of (-1)^(i+1) (which alternates signs) and i (which is just the index itself). The general term (-1)^(i+1) ensures that the sign alternates as the index i increases by 1 each time.