Write each expression in sigma notation.

Question

1 − 2 + 3 − 4 + 5 − 6 + ⋯ − 10

Answer 1

We want the sum of the numbers from 1 to 10. So, k=1 to 10, sum of k.

However, the sign of the numbers alternates between + and -. (-1)^k+1 does that, starting with +1 and alternating with (-1).

S = (+1)(1) + (-1)(2) + (+1)(3) + (-1)(4) + (+1)(5) + (-1)(6) + . . . +(-1)(10)