2 years ago

In a triangle, the measure of the second angle is twice the measure of the first angle. The third angle is equal to the sum

Mathematics

1 answer:

tresset_1 [31]2 years ago

7 0

20bxbsbs z. Sjens ammKzkz

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VashaNatasha [74]

1.1

Hope this helps:)

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3 years ago

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

A jewelry store has 9/10 of an ounce of gold they need to split into one 6 ounce groups how many groups going to make

Mariana [72]

12
12
12
12
12
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2
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12
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2 years ago

Sarah's water bottle holds 500 milliliters. Shawn container holds 4/5 as much water. How many total milliliters of water do both

tamaranim1 [39]

900 milliliters combined

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3 years ago

PLEASE HELP ME, ITS DUE RN

madam [21]

Answer:

here you go

Step-by-step explanation:

35+a+b+c=270

35+a=90

a+b=180

35+90+c=180

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2 years ago