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ICE Princess25 [194]
3 years ago
14

This is literally 20 points of my grade pls help! very desperate.

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0

Answer:

Step-by-step explanation:

see attached

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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 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

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3 years ago
3p + 4r = q solve for p
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Answer:

p = \dfrac{q - 4r}{3}

Step-by-step explanation:

3p + 4r = q

3p = q - 4r

p = \dfrac{q - 4r}{3}

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Step-by-step explanation:

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inessss [21]
Intersecting is where two lines cross at any angle.
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Four people equally share 3/4 of a whole pizza. What fractional part of the whole pizza does each person receive?
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Answer:

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Step-by-step explanation:

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