Infinite

Algebra Level 1

1 4 , 1 4 2 , 1 4 3 , 1 4 4 , 1 4 5 , ⋯ \large \frac{1}{4},\frac{1}{4^{2}}, \frac{1}{4^{3}}, \frac 1{4^4}, \frac 1{4^5}, \cdots

What the sum of the infinite sequence above?

4 4 3 3 1 4 \frac 14 1 3 \frac 13

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Lorenz Navales by lorenz navales , 21, Philippines

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1 solution

Swagat Panda
Aug 14, 2016

Using the formula S ∞ = a 1 − r , where a = 1 4 and r = 1 4 we get : \text{Using the formula } {S_{\infty}={\dfrac{a}{1-r}}} \text{, where } a=\dfrac{1}{4} \text{ and } r=\dfrac{1}{4} \text{ we get :} S ∞ = 1 4 1 − 1 4 = 1 4 3 4 = 1 3 S_{\infty}={\dfrac{\dfrac14}{1-\dfrac14}=\dfrac{\dfrac14}{\dfrac34}}=\dfrac13

7 Helpful 0 Interesting 0 Brilliant 0 Confused

ya your right thanks for your solution..

lorenz navales - 4 years, 10 months ago

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