Question

Find the partial sum.14.(-1)" (2n-1)n=5

Answer 1

This requires us to add up the expression as the variable goes from n = 5 to n = 10.

`(-1)^{n\text{ }}\text{ becomes 1 or -1 if n is even and odd respectively.}`

And we know that when we substitute n between 5 to 10, we get

For n = 5, we have:

-1 x (2(5) -1) = -1 x 9 = -9

For n = 6, we have:

1 x (2(6) -1) = 1 x 11 = 11

For n = 7, we have:

-1 x (2(7) -1) = -1 x 13 = -13

For n = 8, we have:

1 x (2(8) -1) = 1 x 15 = 15

For n = 9, we have:

-1 x (2(9) -1) = -1 x 17 = -17

For n = 10, we have:

1 x (2(10) -1) = 1 x 19 = 19

Next, we add up all.

-9 + 11 + (-13) + 15 + (-17) + (19)= 6

Hence, answer is 6