1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tasya [4]
3 years ago
8

Compute i^1+i^2+i^3....i^99+i^100

Mathematics
1 answer:
fgiga [73]3 years ago
7 0

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:______________________

S=(term1)*\frac{1-(common.ratio)^{number.of.terms}}{1-(common.ratio)}

_______________________________

then

S=i*\frac{1-i^{100} }{1-i}

or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1  (we know that i⁴ = 1)

Hence

S = 0

You might be interested in
Ernesto has already jarred 17 liters of jam and will jar an additional 1 liter of jam every
wlad13 [49]
I think The answer is 45
8 0
3 years ago
In the past year Jenny watched 44 movies that she thought were very good. She watched 55 movies over the whole year. Of the movi
igomit [66]

To solve this problem, we must divide the number of movies that Jenny thought were very good by the total number of movies she watched. This is because we are finding a percentage, which represents a part out of a whole that have a factor, which in this case is very good movies. First, we begin by dividing 44/55. Then, we realize that both the numerator and the denominator are divisible by 11, so if we divided them both by 11 that would simplify the fraction.

44/55 = 44/11 / 55/11 = 4/5

Next, we can now easily divide our simplified fraction.

4/5 = 0.8

Finally, we must multiply by 100, because a percentage is a portion of 100 (the total is 100%). This is equivalent to moving the decimal point two places to the right.

0.8 * 100 = 80%

Therefore, Jenny thinks that 80% of the movies she watched this year were very good.

Hope this helps!

7 0
2 years ago
Bradley is returning home from a place that is 2 kilometers away. The function y = 2,000 − 90x represents Bradley's distance fro
12345 [234]

Answer:

The function is linear

The function changes at a constant rate

Step-by-step explanation:

If this function were to be graphed, a line would be seen. It is not an increasing function because he is getting closer to home so the distance from his house is decreasing

6 0
3 years ago
GIVING BRAINLIEST PLEASE HELPPPPPPPPPPPPP
Anna [14]

Answer:

C

Step-by-step explanation:

The number of tips that the server gets is <em>dependent</em> on how many customers she serves.

Hope this helps!

5 0
2 years ago
Read 2 more answers
What do you think the answer is, please hurry
vazorg [7]
There is an 18% chance that out of the 3 students she asks, 3 would be in a band. I hope this helped ^^
6 0
3 years ago
Other questions:
  • Distance between each pair of points<br> (0.4). (8. -2)
    9·2 answers
  • Which pair of number is relative prime<br><br> 7 and 42<br> 16 and 39<br> 66 and 77 <br> 90 and 891
    12·1 answer
  • What is the reciprocal of 5/8
    10·1 answer
  • X - 5 + 12 + 2x = 4(8 – 11x) + 7(1 + 9x)
    5·2 answers
  • Jason has 65 t-shirts and wants to give away 15% of them to help make room in his closet.
    8·2 answers
  • Three times a number is three more than twice the number. Which equation can be used to find the value of x, the unknown
    10·2 answers
  • Point B lies on AC between A and C. If AB = 8 and AC = 10, find BC.
    13·2 answers
  • A ball is thrown vertically in the air with an initial velocity of 60 feet per second from an initial height of 6 feet. The equa
    15·1 answer
  • While standing on a pier, Lynette saw a balloon floating 20 feet above her and a fish swimming 4 feet below the surface of the w
    14·2 answers
  • HALP PLS Which expressions are equivalent to this expression?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!