Salut! =)
( 9² × 9⁴ × 9⁶ × .... × 9⁸⁰ ) : ( 3 × 3² × 3³ × ... × 3⁵⁰ ) = ?
9² × 9⁴ × 9⁶ × .... × 9⁸⁰
9²⁽¹⁺²⁺³⁺ ⁺⁴⁰ )
1 + 2 + 3 + ... + 40 = [tex]\frac{40 * 41 }{2}[/tex] = 20 × 41 = 820
Folosim formula Sumei Gauss
1 + 2 + 3 + ... + n = [tex]\frac{n ( n + 1 ) }{2}[/tex]
9²ˣ⁸²⁰ = 9¹⁶⁴⁰ = ( 3 ² ) ¹⁶⁴⁰ = 3³²⁸⁰
3 × 3² × 3³ × ... × 3⁵⁰
3¹⁺²⁺³⁺ ⁺⁵⁰ = 3¹²⁷⁵
1 + 2 + 3 + ... + 50 = [tex]\frac{50 * 51 }{2}[/tex] = 25 × 51 = 1275
3³²⁸⁰ : 3¹²⁷⁵ = 3³²⁸⁰⁻¹²⁷⁵ = 3²⁰⁰⁵
R : 3²⁰⁰⁵
Bafta! =)
