Question

calcule a soma S=i+i²+i³+i⁴+...+¹⁰⁰

me ajudem pvf e pra hj!​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{S = i + i^2 + i^3 + i^4 + ... + i^{100}}$

$\mathsf{i^1 = i}$

$\mathsf{i^{100} = (i^2)^{50} = (-1)^{50} = 1}$

$\mathsf{i^2 = -1}$

$\mathsf{i^{99} = i.[\:(i^2)\:]^{49} = i.(-1)^{49} = -i}$

$\mathsf{i^3 = i.i^2 = i.(-1) = -i}$

$\mathsf{i^{98} = [\:(i^2)\:]^{49} = (-1)^{49} = -1}$

$\mathsf{i^4 = (i^2)^2 = (-1)^2 = 1}$

$\mathsf{i^{97} = i.[\:(i^2)\:]^{48} = i.(-1)^{48} = i}$

$\boxed{\boxed{\mathsf{S = i + i^2 + i^3 + i^4 + ... + i^{100} = 0}}}$