Find the sum of the infinite series1/3+4/9+16/2764/81... if it exists.

Mathematics

1 answer:

nata0808 [166]4 years ago

8 0

Answer:

It does not exist.

Step-by-step explanation:

If we divide the second term by the first, 3rd by the 2nd and the 4th by the 3rd we get a constant result 4/3.

So this is a Geometric Series with common ratio r = 4/3 and a1 = 1/3.

As the common ratio is greater than 1 the series diverges ( continues to get bigger) so there is no sum to infinity. It just goes on getting bigger and bigger without bounds.

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<h3>What is Triangle?</h3>

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All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

given that

let the height of the triangle be x

then the width is x-3

Area = $\frac{height \times length}{2}$