Question

The value of r such that 1+r²+r³...=¾

Answer 1

Answer:

by applying formula of infinite sum of GP,

3/4 = 1/(1-r)

4 = 3-3r

r = 3/7

Answer 2

The value of r is $\dfrac{-1}{3}$

Step-by-step explanation:

Since we have given that

$1+r^2+r^3...=\dfrac{3}{4}$

It forms a Geometric series:

So, here, a = 1

Common ratio would be $\dfrac{r^3}{r^2}=r$

So, the sum of infinite series would be

$\dfrac{a}{1-r}=\dfrac{3}{4}\\\\\dfrac{1}{1-r}=\dfrac{3}{4}\\\\4=3(1-r)\\\\4=3-3r\\\\4-3=-3r\\\\1=-3r\\\\r=\dfrac{-1}{3}$

Hence, the value of r is $\dfrac{-1}{3}$

# learn more:

8(1/r^3+1/r+r+r^3)=85.find the value of r

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