Find a formula for the sum of the first n even positive integers.
1 answer:
So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct
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The range of the function shown on the graph (see attachment) is: D. -9 ≤ y ≤ 8.
<h3>What is a range?</h3>A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.
<h3>How to identify the range of this graph?</h3>The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached below, we can reasonably infer and logically deduce the following:
Range = [-9, 8]
In interval notation, the range of this graph can be rewritten as -9 ≤ y ≤ 8.
Read more on range here: brainly.com/question/16610662
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<u>Complete Question:</u>
Select the correct answer.
A graph plots two points at (negative 7, 8) and (negative 2, negative 9) on the x y coordinate plane. A diagonal curve connects both points.
What is the range of the function shown on the graph above?
A. -7≤y≤-2
B.-8≤y≤8
C.-2≤y≤-7
D. -9≤y≤8
