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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

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Answer:

20

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
I need help please and thanks
Akimi4 [234]
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7 0
3 years ago
please help! a. they share a vert. asymptote at x=-2 | b. they share a horizontal asymptote at y=-.5 | c. they share an oblique
Rashid [163]
They share a horizontal asymptote at y=-.5

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3 0
3 years ago
| 1. Add the polynomials.<br> (-14x2 + 6x – 5) + (x3 + 2x2 + 5)
docker41 [41]

Answer:

So I'm not completely sure what the x is standing for in this. Is it standing at a multiplication sign like -14 TIMES 2? Or is it -14x TIMES 2?

Step-by-step explanation:

7 0
3 years ago
I need help with this problem
Anarel [89]

The midpoint lines are half the opposite side length.

Line DE is given as 7 , So Line F = 7 x 2 = 14

Line EF is given as 12, so Line D = 12 x 2 = 24

Line DF is given as 16, so line E = 16 x 2 = 32


The perimeter is the sum of the 3 sides:

Perimeter = 14 + 24 + 32 = 70

6 0
3 years ago
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