Question

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

Answer 1

Answer:as in a sum notation

Explanation:

Answer 2

The answer is
`\sum_(n=0)^(\infty)(-1)^n3^n`

Step-by-step explanation:

Given the pattern 1 - 3 + 9 - 27 + ...

we have to write the sum using summation notation.

As,
`1=(-1)^(0)3^0`

`-3=(-1)^(1)3^1`

`9=(-1)^(2)3^2`

`-27=(-1)^(3)3^3`

hence, we can write

1 - 3 + 9 - 27 + ...

=
`(-1)^(0)3^0+(-1)^(1)3^1+(-1)^(2)3^2+(-1)^(3)3^3+.....`

=
`\sum_(n=0)^(\infty)(-1)^n3^n=\sum_(n=0)^(\infty)(-3)^n`

which is required sigma notation.