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3 years ago

5

Jillian wants to figure out how much water will fit inside the water tower that is by her house. So she wants to find the volume

of the water tower. True or false?

1 answer:

grigory [225]3 years ago

4 0

Answer:

I'm going to say true because that's the most logical answer

Step-by-step explanation:

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

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3 years ago

1/2ac2 where a =5 and b=2

Evgen [1.6K]

I’ll assume the c is b. (1/2) x (5) x (2) x (2) is 10

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Answer:

Step-by-step explanation:

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d = ¾m = 0.75m

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3 years ago

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Answer:

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Yes it is a geometric sequence and the common ratio is 2/3

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