Good morning ☕️
Answer:
<h3>i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰ =
0</h3>
Step-by-step explanation:
Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰
S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰
S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀
then, S is the sum of 100 consecutive terms of a geometric sequence (an)
where the first term a1 = i¹ = i and the common ratio = i
FORMULA:______________________
_______________________________
then
or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)
Hence
S = 0
22.
pythagorean theorem says legs a and b and hypotenuse c of a right triangle are related via the equation c²=a²+b². in other words, adding the sum of the squares of the legs get you the square of the hypotenuse
if the hypotenuse is 4 meters long, c = 4.
if one leg is 3 meters long, we can choose either a or b to be 3. it does not really matter. let us choose a = 3. now we have to find b.
if we have c²=a²+b², we can solve for b.
subtract a² both sides to get c²-a²=b², and then square root both sides to get
b = √(c²-a²)
plugging in our info we get
b = √(4²-3²) = √(16 -9) = √7
so the answer is √7 meters for 22
23
two triangles are similar, then the proportion of their sides are the same. the propotion between the smaller triangles' hypotenuse and 2cm leg is 5cm/3cm.
notice how the bigger triangle just have a doubled hypotenuse. therefore, the bigger triangle's x and y are just the corresponding smaller triangle values doubled.
x = 6 and y = 8
