Answer:
24/49
Step-by-step explanation:
Let's add the terms and see if there's a pattern
![\dfrac{1}{1\times 3}+\dfrac{1}{3\times 5}=\dfrac{5+1}{1\times 3\times 5}=\dfrac{2}{5}\quad\text{sum of 2 terms}\\\\\dfrac{2}{5}+\dfrac{1}{5\times 7}=\dfrac{14+1}{5\times7}=\dfrac{3}{7}\quad\text{sum of 3 terms}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B1%5Ctimes%203%7D%2B%5Cdfrac%7B1%7D%7B3%5Ctimes%205%7D%3D%5Cdfrac%7B5%2B1%7D%7B1%5Ctimes%203%5Ctimes%205%7D%3D%5Cdfrac%7B2%7D%7B5%7D%5Cquad%5Ctext%7Bsum%20of%202%20terms%7D%5C%5C%5C%5C%5Cdfrac%7B2%7D%7B5%7D%2B%5Cdfrac%7B1%7D%7B5%5Ctimes%207%7D%3D%5Cdfrac%7B14%2B1%7D%7B5%5Ctimes7%7D%3D%5Cdfrac%7B3%7D%7B7%7D%5Cquad%5Ctext%7Bsum%20of%203%20terms%7D)
Suppose we say the sum of n terms is (n/(2n+1)), the next term in the series will be 1/((2n+1)(2n+3)) and adding that to the presumed sum gives ...
![\dfrac{n}{2n+1}+\dfrac{1}{(2n+1)(2n+3)}=\dfrac{n(2n+3)+1}{(2n+1)(2n+3)}=\dfrac{2n^2+3n+1}{(2n+1)(2n+3)}\\\\=\dfrac{(2n+1)(n+1)}{(2n+1)(2n+3)}=\dfrac{n+1}{2n+3}\text{ matches }\dfrac{(n+1)}{2(n+1)+1}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%7D%7B2n%2B1%7D%2B%5Cdfrac%7B1%7D%7B%282n%2B1%29%282n%2B3%29%7D%3D%5Cdfrac%7Bn%282n%2B3%29%2B1%7D%7B%282n%2B1%29%282n%2B3%29%7D%3D%5Cdfrac%7B2n%5E2%2B3n%2B1%7D%7B%282n%2B1%29%282n%2B3%29%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%282n%2B1%29%28n%2B1%29%7D%7B%282n%2B1%29%282n%2B3%29%7D%3D%5Cdfrac%7Bn%2B1%7D%7B2n%2B3%7D%5Ctext%7B%20matches%20%7D%5Cdfrac%7B%28n%2B1%29%7D%7B2%28n%2B1%29%2B1%7D)
Then it appears the sum of n terms is (n/(2n+1)). So, the sum of 24 terms is ...
![S_{24}=\dfrac{24}{2\times24+1}=\boxed{\dfrac{24}{49}}](https://tex.z-dn.net/?f=S_%7B24%7D%3D%5Cdfrac%7B24%7D%7B2%5Ctimes24%2B1%7D%3D%5Cboxed%7B%5Cdfrac%7B24%7D%7B49%7D%7D)
Y = x + 3 is the answer
the y-intercept is 3, so the answer should have a "+ 3" in it
when you are trying to determine the gradient (the x), you can use two methods
first method:
picture/sketch the line. If the line is going upwards (from left to right), it's positive. If the line is going downwards (from left to right), it's negative. However, this method only works for this question, you should try using the second method more
second method:
use the formula: (y - y) / (x - x)
So, you use the y from one of the brackets and subtract the y from the other bracket. Then, you put it over the x ,from the same bracket as the first y, and subtract the x from the second bracket. If you are confused, look at the picture. (Sorry for the messy explanation)
Answer:
4x + 4
Step-by-step explanation:
perimeter= breadth + length + breadth + length
(x+2)+(x+2)+x+x
= 4x(because there is 4 x) + 2 +2
= 4x + 4
(12x40)+(18x6)
or
(12x40)+(18x6)=588
thank you for letting me answer and god bless <3
Answer:
4. It should be less than coefficient on str in the first regression
Step-by-step explanation:
Since the str and income are positively correlated and the coefficient on income in the second regression is positive, the coefficient on str in the second regression therefore should be less than coefficient on str in the first regression.