Question

Evaluate, and round your answer to the nearest hundredth.

Answer 1

Answer:

  (d)  -1.83

Step-by-step explanation:

The explicit expression for the sum is ...

  S = (-11/5)×(1 -(-1/5)^10)/(1 -(-1/5)) = -2.2(1 -1.024×10^-7)/1.2

  S = -1.8333331456

The sum is approximately -1.83.

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Additional comment

For a sum of a sequence with multiplier 'a' and common ratio r, we find ...

  $\displaystyle S=\sum_{n=1}^{10}ar^n=ar+ar^2+ar^3+\dots+ar^{10}\\\\rS=ar^2+ar^3+\dots+ar^{10}+ar^{11}\\\\S-rS=ar+(ar^2-ar^2)+(ar^3-ar^3)+\dots+(ar^{10}-ar^{10})-ar^{11}\\\\S=\dfrac{ar-ar^{11}}{1-r}=ar\dfrac{1-r^{10}}{1-r}$

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A calculator or spreadsheet can also find the sum for you.