sigma notation problem

[Nitai]

How do you write the equation
S=0.6(1.5^2+1.5^2.6'1.5^2.3+1.5^3.2+1.5^3.8+1.5^4.4)
using Sigma Notaion?
and what is the domain of the variable?
and how can i tell if they were summing left or right handed rectangles when figuring out the area under the curve?

 

[pka]

\(\displaystyle \L
\sum\limits_{k = 0}^4 {\left( {.6} \right)\left( {1.5} \right)^{2 + .6k} }\)

 

[soroban]

Hello, Nitai!

Is there more to the problem?
\(\displaystyle \;\;\)Without more information, there are no unique answers.

How do you write: \(\displaystyle \L\,S\;=\;0.6\left(1.5^2\,+\,1.5^{2.6}\,+\,1.5^{3.2}\,+\,1.5^{3.8}\,+\,1.5^{4.4}\right)\) using Sigma Notaion?

pka gave one possible answer . . .

I have another: \(\displaystyle \L\,\sum^5_{k=1}(0.6)(1.5)^{1.4+0.6k}\)

What is the domain of the variable?

pka's domain is: \(\displaystyle \{0,\, 1,\, 2,\, 3,\, 4\}\) . . . mine is: \(\displaystyle \{1,\, 2,\, 3,\, 4,\, 5\}\)

and how can i tell if they were summing left- or right-handed rectangles
when figuring out the area under the curve?

Assuming that the inverval is \(\displaystyle [0,\,5]\),

\(\displaystyle \;\;\)pka is summing left-endpoints;

\(\displaystyle \;\;\)I am summing right endpoints.

 

[pka]

In any event, wouldn’t the interval be \(\displaystyle [2,5]\) or \(\displaystyle [1.4,4.4]\)???