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4 years ago

What must be true to find the sum of a infinite sequence?

Mathematics

1 answer:

Georgia [21]4 years ago

3 0

Answer:

The series must be decreasing, and the limit as the n-th term goes to infinity should be 0.

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2. Suppose (220)_b and (251)_b are the squares of consecutive integers. Determine b.

Andrei [34K]

Let $x$ and $x+1$ be these consecutive integers. For some base $b$ , we can write

$(x_{10})^2=220_b=2b^2+2b$

$((x+1)_{10})^2=251_b=2b^2+5b+1$

$x^2=2b^2+2b$

then

$x^2+1=2b^2+2b+1$

Now,

$x^2+2x+1=2b^2+5b+1$

$2x+2b^2+2b+1=2b^2+5b+1$

$\implies2x=3b$

Squaring both sides gives

$4x^2=9b^2$

and so

$4(2b^2+2b)=9b^2$

$\implies8b^2+8b=9b^2$

$\implies b^2-8b=0\implies\boxed{b=8}$

(because the base has to be non-zero)

3 0

3 years ago

Fifteen tickets cost $193.75. What is the average cost of each ticket?

julsineya [31]

Answer:

about $12.92

Step-by-step explanation:

could be wrong though

8 0

3 years ago

Read 2 more answers

Help <br> Fjfjdjxjcjfjfjdjdjjdjdjd

White raven [17]

Answer:

a or b

Step-by-step explanation:

3 0

3 years ago

Solve the following inequality.

Luden [163]

First simplify.
$-\frac{2}{3}x \ \textgreater \ \mathrm{Multiply\:fractions}:\ \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c} \ \textgreater \ -\frac{2x}{3}$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)} \ \textgreater \ \ \textgreater \ \frac{2x}{3}\ \textless \ -8$

$\mathrm{Multiply\:both\:sides\:by\:}3 \ \textgreater \ \frac{3\cdot \:2x}{3}\ \textless \ 3\left(-8\right) \ \textgreater \ Simplify \ \textgreater \ 2x\ \textless \ -24$

$\mathrm{Divide\:both\:sides\:by\:}2 \ \textgreater \ \frac{2x}{2}\ \textless \ \frac{-24}{2} \ \textgreater \ Simplify \ \textgreater \ x\ \textless \ -12$

$Therefore\; x\ \textless \ -12 \;is\;our\;answer!$

Hope this helps!

7 0

3 years ago

Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions a

grandymaker [24]

Answer:

it b

Step-by-step explanation:

3 0

3 years ago