Răspuns:
Explicație pas cu pas:
a) calculam mai intai suma
s=9+9²+9³+...+9ⁿ⁻¹
9·S= 9²+9³+...+9ⁿ⁻¹+9ⁿ, Scadem prima din a doua
9S-S=9²+9³+...+9ⁿ⁻¹+9ⁿ - (9+9²+9³+...+9ⁿ⁻¹)=9ⁿ-9, ⇒
8S=9ⁿ-9, atunci
x-9=8S, ⇒x=9ⁿ-9 + 9 =9ⁿ.
b) S=25+25²+25³+...+25ⁿ⁻¹
25S= 25²+25³+...+ 25ⁿ⁻¹+25ⁿ
25S-S=24S=25²+25³+...+ 25ⁿ⁻¹+25ⁿ - (25+25²+25³+...+25ⁿ⁻¹)=25ⁿ - 25
atunci x-25=24S=25ⁿ - 25, ⇒x=25ⁿ - 25+25=25ⁿ.
c) S=16+16²+16³+...+16ⁿ⁻¹
16S= 16²+16³+...+16ⁿ⁻¹+16ⁿ,
16S-S=15S=16²+16³+...+16ⁿ⁻¹+16ⁿ-(16+16²+16³+...+16ⁿ⁻¹)=16ⁿ-16.
x-16=15S=16ⁿ-16, ⇒x=16ⁿ-16+16=16ⁿ.
d) S=4+4²+4³+...+4ⁿ⁺²
4S= 4²+4³+...+4ⁿ⁺²+4ⁿ⁺³
4S-S=3S=4²+4³+...+4ⁿ⁺²+4ⁿ⁺³-(4+4²+4³+...+4ⁿ⁺²)=4ⁿ⁺³-4
x-4=3S=4ⁿ⁺³-4, ⇒x=4ⁿ⁺³-4+4=4ⁿ⁺³
