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
What percent of 12 is 48<br> A. 0.25%<br> B. 4% <br> C. 25%<br> D. 40% <br> E. 400%
Step2247 [10]

Answer: the answer is 25 percent

Step-by-step explanation: 25 percent times 48 is 12

5 0
2 years ago
The fourth question please.
garik1379 [7]
Going from the left to the right. 9, 4, 13, 15, 12, 6, 11. The total cost is the sum of these, or $70,000.
8 0
3 years ago
The manager of the BiLo Supermarket in Mt. Pleasant, Rhode Island, gathered the following information on the number of times a c
pishuonlain [190]

Answer: kindly check explanation

Step-by-step explanation:

Given the data :

5 3 3 1 4 4 5 6 4 2 6 6 6 7 1 1 14 1 2 4 4 4 5 6 3 5 3 4 5 6 8 4 7 6 5 9 11 3 12 4 7 6 5 15 1 1 10 8 9 2 12

Frequency and relative frequency table can be found in the attachment below.

b. Where do the data tend to cluster?

3 up to 6

7 0
3 years ago
What is the length of the arc intercepted by an angle of 10 degrees on a circle with a radius of 10 meters?
soldier1979 [14.2K]
   
\displaystyle\\&#10;\texttt{Length of the arc }= 2\pi R\times  \frac{10}{360} = \frac{2\pi \times 10}{36} = \frac{20\pi}{36} =  \boxed{\frac{5\pi}{9}~m}



3 0
2 years ago
What is the scale factor for pre-image IJKH to image MNOL?
solniwko [45]

Answer:

Step-by-step explanation:

Given are two rectangles MNOL and IJKH

MNOL is the image and IJKH is the preimage.

OBviously similarity is preserved between these.

Hence sides will be proportional

i.e. l1/l2 = w1/w2 = Scale factor k

This can also be written as

Scale factor square = k^2=\sqrt{ \frac{areaI}{area2} }

Scale factor = square root of ratio of rectangle areas

Find ratio as

\frac{375}{135} =\frac{25}{9}

k = Scale factor = square root of the above fraction

=\frac{5}{3}

5 0
3 years ago
Other questions:
  • Find the quotient.<br> thank you
    7·2 answers
  • How do I simplify 5x + -2x + 6x + -x + 3x + 15x. ?
    7·1 answer
  • 1.<br>If I have £400 and I give 15% of the total to charity, how much does the charity<br>receive?​
    11·1 answer
  • Randy walks his dog each morning. He walks StartFraction 7 Over 12 EndFraction of a mile in 7 minutes. How many miles does he wa
    13·2 answers
  • Find a 3 digit number with all these properties: all 3 digits are different, the 1st digit is the square of the second digit in
    14·1 answer
  • ANy help i'll give brainliest
    14·2 answers
  • Mrs. Murphy earns a 3.5% commission at her job in retail. How much does she need to sell in order to earn $630
    10·2 answers
  • Whats 100x20x40 if you get it you get mark brainly
    11·2 answers
  • A sketch is drawn that is 6 inches by 9 inches. It is put in a frame of uniform width. If the area of the sketch is
    7·1 answer
  • The temperature was 75 degrees. at noon, the temperature increased by 7. by evening the temperature decreased by 7
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!