Question

Find the infinite sum, if it exists for this series: −3+ (1.2) + (−0.48)+⋯

Answer 1

The series is given below as

`-3+(1.2)+(-0.48)+.....`

Step 1:

We will calculate the common ratio

`\begin{gathered} r=(a_2)/(a_1)=(a_3)/(a_2) \\ r=(1.2)/(-3)=-(0.48)/(1.2) \\ r=-0.4 \end{gathered}`

The sum of infinite series will be calculated using the formula below

`\begin{gathered} S_(\infty)=(a)/(1-r) \\ S_(\infty)=-(3)/(1-(-0.4)) \\ S_(\infty)=-(3)/(1+0.4) \\ S_(\infty)=-(3)/(1.4) \\ S_(\infty)=-3*(10)/(14) \\ S_(\infty)=-(30)/(14) \end{gathered}`

Hence,

The final answer is

`\Rightarrow-(30)/(14)`