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3 years ago

2, 5, 11, 23, , , _, _, ______. Conjecture:

Mathematics

1 answer:

lisov135 [29]3 years ago

4 0

Answer:

2, 5, 11, 23, 47, 95, 191, 383, 767.

Step-by-step explanation:

This sequence is 2, 5, 11, 23, 47, 95, 191, 383, 767 because as you may notice, 2+ 3 =5, double the 3 to get 6. 5+ 6 =11, double the 6 to get 11 + 12 =23, etc.

Double the factor and add it to the previous term to get your next term and so forth.

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Write out the first few terms of the series Summation from n equals 0 to infinity (StartFraction 2 Over 3 Superscript n EndFract

anyanavicka [17]

Answer:

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = 15/8$

Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

$\sum\limits_{n = 0}^{\infty} a*r^n$ you have that

$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

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3 years ago

1. FRUITS Find the ratio of bananas to oranges in the graphic at the right. Write the

podryga [215]

Answer:

999kkk b8llion

Step-by-step explanation:

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3 years ago

PLEASE HELP!! QUICK. MULTIPLE CHOICE

melisa1 [442]

Question 3 answer is C

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4 years ago

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Simplify (-3c^-3w^5)^3<br> A -9w^8<br> B. -27cw^8<br> C. w^15/27c^9<br> D.-27w^15/c^9

kenny6666 [7]

Answer:

$\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}$

Step-by-step explanation:

$(-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}$

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3 years ago

Evaluate 32 - 4 ^ 2 ÷ 4

netineya [11]

Answer:

Step-by-step explanation: 32 - 4 ^2 /4

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4 years ago

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2, 5, 11, 23, ____, ______, _______, _______, ________. Conjecture:​

2, 5, 11, 23, , , _, _, ______. Conjecture: