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:______________________
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then
or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)
Hence
S = 0
I agree only if you have even powers -- even negative ones.
1/i^2 = 1/-1 = - 1
i^0 also gives 1 So far no problem.
It is when you consider the odd numbers that you don't get 1 or -1
You get either -i or i
i^(4n + 1) = i
i^(4n - 1) = -i
Market value = $310,000
Since market value for tax purposes is 40% of the actual market value,
Market value for tax assessment = $310,000*40% = $124,000
Tax rate per $1000 of assessed valuation = $145.10 or 14.51% of the assessed value
Hence tax to be paid by leo = $124000*14.51% = $17992.40
