Question

Write the sum using summation notation, assuming the suggested pattern continues.1 - 3 + 9 - 27 + ...

Answer 1

The pattern that is summed may be written as
S = 1 - 3 + 9 - 27 + . . .
= (-3)^0 + (-3)^1 + (-3)^2 + (3)^3 + . . .

The n-th term in the sum is (-3)^n, for n = 0,1,2,3, . . .

The sum may be written with summation notation as

`\Sigma\limits^ { }_(k=0) {(-3)^k} \,`