Question

Answer 1

a: \(A=3+3^2+3^3+...+3^{100}\)

=>\(3A=3^2+3^3+3^4+...+3^{101}\)

=>\(3A-A=3^{101}+3^{100}+...+3^4+3^3+3^2-3^{100}-3^{99}-...-3^2-3\)

=>\(2A=3^{101}-3\)

=>\(A=\dfrac{3^{101}-3}{2}\)

b: \(n+7⋮n+2\)

=>\(n+2+5⋮n+2\)

=>\(n+2\inƯ\left(5\right)\)

=>\(n+2\in\left\{1;-1;5;-5\right\}\)

=>\(n\in\left\{-1;-3;3;-7\right\}\)

mà n là số tự nhiên

nên n=3

Answer 2

a: A=3+32+33+...+3100�=3+32+33+...+3100

=>3A=32+33+34+...+31013�=32+33+34+...+3101

=>3A−A=3101+3100+...+34+33+32−3100−399−...−32−33�−�=3101+3100+...+34+33+32−3100−399−...−32−3

=>2A=3101−32�=3101−3

=>