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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:

First we must learn to dissect a question.

<h3>Explanation:</h3>

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Step-by-step explanation:

The reason why it would be wrong is because the amount of points lost was less than the total amount of points gained.

In week one and two the company gained 9 1/2 points and 6 5/8 points. When you add them together, you get 16 1/8 points.

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Answer:

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Step-by-step explanation:

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