Answer: 
; 5
Step-by-step explanation:
Given series : ![[\dfrac{5}{1\cdot2}]+[\dfrac{5}{2\cdot3}]+[\dfrac{5}{3\cdot4}]+....+[\dfrac{5}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=%5B%5Cdfrac%7B5%7D%7B1%5Ccdot2%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B2%5Ccdot3%7D%5D%2B%5B%5Cdfrac%7B5%7D%7B3%5Ccdot4%7D%5D%2B....%2B%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Sum of series = ![S_n=\sum^{\infty}_{1}\ [\dfrac{5}{n\cdot(n+1)}]=5[\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}]](https://tex.z-dn.net/?f=S_n%3D%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5C%20%5B%5Cdfrac%7B5%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D%3D5%5B%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%5D)
Consider 
⇒ ![S_n=5\sum^{\infty}_{1}\dfrac{1}{n\cdot(n+1)}=5\sum^{\infty}_{1}[\dfrac{1}{n}-\dfrac{1}{n+1}]](https://tex.z-dn.net/?f=S_n%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5Cdfrac%7B1%7D%7Bn%5Ccdot%28n%2B1%29%7D%3D5%5Csum%5E%7B%5Cinfty%7D_%7B1%7D%5B%5Cdfrac%7B1%7D%7Bn%7D-%5Cdfrac%7B1%7D%7Bn%2B1%7D%5D)
Put values of n= 1,2,3,4,5,.....n
⇒ 
All terms get cancel but First and last terms left behind.
⇒
Formula for the nth partial sum of the series :
Also, 
Four quarters,ten dimes,twenty nickels,100 pennies
(b)
The 50 degree angle and angle b are vertical angles, which means they are congruent.
The 50 degree angle and angle c are a linear pair, which means that they are supplementary/add up to 180 degrees.
Angles a and c are vertical angles, which means they are congruent.
a = 130
b = 50
c = 130
(c)
The 90 degree angle and angle b are vertical angles, which means they are congruent.
The 50 degree angle and angle c are vertical angles, which means they are congruent.
The 50 degree angle, 90 degree angle, and angle d all form a line, which means that they are supplementary and add up to 180.
Angle d and angle a are vertical angles, which means they are congruent.
a = 40
b = 90
c = 50
d = 40
(e)
The measure of a circle is 360 degrees. These three angles form a circle, so therefore if we add them all up, they will equal 360 degrees.
3a + 4a + 5a = 360
12a = 360
a = 30
(f)
The measure of a circle is 360 degrees. These four angles form a circle, so therefore if we add them all up, they will equal 360 degrees.
3a + 4a + 5a + 6a = 360
18a = 360
a = 20
Hope this helps!! :)
Answer:
( -1.5, -1)
Step-by-step explanation:
add the x values together and divide by 2 and add the y values together and divide by 2
x: -6 + 3 = -3 divided by 2 x = -1 1/2 or -1.5
y: 5 + (-7) = -2 divided by 2 y = -1
