Answer:
The answer is [tex]\sum_{n=0}^{\infty}(-1)^n3^n[/tex]
Step-by-step explanation:
Given the pattern 1 - 3 + 9 - 27 + ...
we have to write the sum using summation notation.
As, [tex]1=(-1)^{0}3^0[/tex]
[tex]-3=(-1)^{1}3^1[/tex]
[tex]9=(-1)^{2}3^2[/tex]
[tex]-27=(-1)^{3}3^3[/tex]
hence, we can write
1 - 3 + 9 - 27 + ...
= [tex](-1)^{0}3^0+(-1)^{1}3^1+(-1)^{2}3^2+(-1)^{3}3^3+.....[/tex]
= [tex]\sum_{n=0}^{\infty}(-1)^n3^n=\sum_{n=0}^{\infty}(-3)^n[/tex]
which is required sigma notation.
