Chapter 11.5, Problem 4OE

To determine

To calculate:

Value of $S_5$ for given series.

Answer to Problem 4OE

Value $S_5$ for given series is $19.94$ .

Explanation of Solution

Give information:

  $7+5+3+1+\mathrm{....}$

Calculation:

Given series is,

  $7+5+3+1+\mathrm{....}$

For finding $S_5$ formula used is ,

  $S_n=a_1{\left(\frac{1-r^n}{1-r}\right)}^n,r\ne 1$

Where,

  $S_n=$ Partial sum.

  $a_1=$ First term.

  $r=$ common ratio.

Initially find out common ratio,

  $\begin{array}{l}r=\frac{5}{7}\\ r=0.714\end{array}$

To find $S_5$ ,

  $S_n=a_1{\left(\frac{1-r^n}{1-r}\right)}^n,r\ne 1$

Substitute the values,

  $\begin{array}{l}{S}_5=7\left(\frac{1-{\left(0.714\right)}^5}{1-\left(0.714\right)}\right)\\ S_5=7\left(\frac{1-\left(0.185\right)}{0.286}\right)\\ S_5=7\left(\frac{0.815}{0.286}\right)\\ S_5=7\left(2.84\right)\\ S_5=19.94\end{array}$

Therefore, value $S_5$ for given series is $19.94$ .