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
Answer:
The number is 5
Step-by-step explanation:
If we need to find the hidden number, Which for simplicity's sake we will denote as "n", lets first write out the equation.
"2 x [n + (-3)] = 4"
We can work through this problem backwards. if we need two times the sum of "n" and (-3) to get to 4, the only number that can be multiplied by 2 to get a product of 4 is 2, so "n" + (-3) must equal 2. so, From here, we can figure out that since 5 + (-3) equals 2, "n" Must equal 5. so, if we plug in 5 for "n" the equation looks like this:
"2 x [5 + (-3)] = 4"
So, since the equation makes sense, the answer is, "n = 5"
Step-by-step explanation:
Since ,
Money lended =$400
Intetest =27.74%
Therefore,
Intetrst=p×r×t/100,if interested monthly
=400×27.74×1/100(interested monthly)
=4×27.74
=$110.96
Interest=p×r×t/100×1/12,if interested anually
=400×27.74×1/100/12
=110.96/12
=$9.24 or it will be $110.96 if it is interested anuaaly..
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Answer:
71°
Step-by-step explanation:
3x° + (x - 11)° + (2x - 55)° = 360°
3x + x - 11 + 2x - 55 = 360°
6x - 66 = 360°
6x = 360° + 66°
6x = 426°
x = 71°