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Mathematics

1 answer:

bulgar [2K]2 years ago

3 0

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABC and DEC. In these triangles,

$\overline{BC}\cong \overline {EC}$ - given
$\overline{AC}\cong \overline {DC}$ - given;
$\angle ACB\cong \angke DCE$ as vertical angles.

So,

$\triangle ABC\cong \triangle DEC$ by SAS postulate (two sides and angle between these sides of one triangle are congruent to two sides and angle between these sides of another triangle, so triangles are congruent).

Congruent triangles have congruent corresponding parts, hence,

$\overline{BA}\cong \overline{ED}$

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Infinite over E n=1 4(0.5)^n-1

yan [13]

Answer:

S = 8

Step-by-step explanation:

An infinite geometric series is defined as limit of partial sum of geometric sequences. Therefore, to find the infinite sum, we have to find the partial sum first then input limit approaches infinity.

However, fortunately, the infinite geometric series has already set up for you. It’s got the formula for itself which is:

$\displaystyle \large{\lim_{n\to \infty} S_n = \dfrac{a_1}{1-r}}$

We can also write in summation notation rather S-term as:

$\displaystyle \large{\sum_{n=1}^\infty a_1r^{n-1} = \dfrac{a_1}{1-r}}$

Keep in mind that these only work for when |r| < 1 or else it will diverge.

Also, how fortunately, the given summation fits the formula pattern so we do not have to do anything but simply apply the formula in.

$\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{1-0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = \dfrac{4}{0.5}}\\\\\displaystyle \large{\sum_{n=1}^\infty 4(0.5)^{n-1} = 8}$