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svetoff [14.1K]
3 years ago
15

Simplify the expression please show work and detail 4m-8/4-2m

Mathematics
1 answer:
Mars2501 [29]3 years ago
5 0
Divide each term in 4m < -8 by 4.
4m/4 < -8/4
Then reduce the expression by cancelling the common factors. 
m < -8/4
Simplify the right side of the equation.
Divide 8 by 4 to get 2.
m < -1*2
Multiply -1 by 2 to get -2
m < -2


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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}

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If k=-\frac45, then

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If k=\frac15, then

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Consider the nth 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

7 0
3 years ago
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