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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
The answer to the given question is as below:-
Polynomials:-
x³-7x²+9x-5x⁴-20
x⁵-5x⁴+4x³+2x-1
3x²-5x⁴+2x-12
Non-polynomial:-
x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.
So the table will be formed as:-
Polynomials:- Non-polynomial:-
x³-7x²+9x-5x⁴-20 x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
x⁵-5x⁴+4x³+2x-1
3x²-5x⁴+2x-12
Therefore the polynomials and non-polynomials are shown in the table above.
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