Find the sum of the following infinite geometric series, if it exists.

Mathematics

2 answers:

FinnZ [79.3K]3 years ago

5 0

S=Asub1/1-r
=1.02/1-2
=1.02/-1
=-1.02

Paha777 [63]3 years ago

4 0

<span>Indefinite pronouns may replace nouns used as subjects, predicate nouns, direct objects, indirect objects, objects of a preposition, and appositives.</span>

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For what value of c does x^2−2x−c=4 have exactly one real solution?<br> PLEASE HELP!!!!!!!

Paul [167]

Answer:

-5

Step-by-step explanation:

Moving all terms of the quadratic to one side, we have

$x^2-2x-(c+4)=0$ .

A quadratic has one real solution when the discriminant is equal to 0. In a quadratic $ax^2+bx+d$ , the discriminant is $\sqrt{b^2-4ad}$ .

(The discriminant is more commonly known as $\sqrt{b^2-4ac}$ , but I changed the variable since we already have a $c$ in the quadratic given.)

In the quadratic above, we have $a=1$ , $b=-2$ , and $d=-(c+4)$ . Plugging this into the formula for the discriminant, we have

$\sqrt{(-2)^2-4(1)(-(c+4))$ .

Using the distributive property to expand and simplifying, the expression becomes

$\sqrt{4-4(-c-4)}=\sqrt{4+4c+16}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{20+4c}\\~~~~~~~~~~~~~~~~~~~~~~=\sqrt{4}\cdot\sqrt{5+c}\\~~~~~~~~~~~~~~~~~~~~~~=2\sqrt{c+5}.$