Question

6EvaluateΣ(1)Round your answer to the nearest hundredth.=1O A -0.01B. 5.25O C. -1.750 D. 10.50W

Answer 1

As given by the question

There are given that the function:

`\sum ^6_(i\mathop=1)7(-(1)/(3))^i`

Now,

To evaluate the given summation:

`\sum ^6_{i\mathop{=}1}7(-(1)/(3))^i=7(-(1)/(3))^1+7(-(1)/(3))^2+7(-(1)/(3))^3+7(-(1)/(3))^4+7(-(1)/(3))^5+7(-(1)/(3))^6`

Then,

`\begin{gathered} \sum ^6_{i\mathop{=}1}7(-(1)/(3))^i=7(-(1)/(3))^1+7(-(1)/(3))^2+7(-(1)/(3))^3+7(-(1)/(3))^4+7(-(1)/(3))^5+7(-(1)/(3))^6 \\ =-(7)/(3)+(7)/(9)-(7)/(27)+(7)/(81)-(7)/(243)+(7)/(729) \\ =-2.33+0.77-0.259+0.086-0.0288+0.0096 \end{gathered}`

Then,

`\begin{gathered} -2.33+0.77-0.259+0.086-0.0288+0.0096=-1.7522 \\ =-1.75 \end{gathered}`

Hence, the correct option is C.