Question

(3¹×3²×3³×....×3⁸⁰)÷(3¹×3³×3⁵×...×3¹¹¹) dau coroana
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Answer 1

(3¹×3²×3³×....×3⁸⁰)÷(3¹×3³×3⁵×...×3¹¹¹)  = ?

1+2+3+...+80=80*81/2=40*81=3240

1+3+5+...+111=(2*0+1)+(2*1+1)+(2*2+1)+...+(2*55+1)=2(1+2+....+55)+56*1=2*55*56/2+56=55*56+56=56*56=3136

(3¹×3²×3³×....×3⁸⁰)÷(3¹×3³×3⁵×...×3¹¹¹)=3¹⁺²⁺³⁺₋₋⁺⁸⁰÷3¹⁺³⁺⁵⁺⁻⁻⁺¹¹¹=3³²⁴⁰÷3³¹³⁶=3³²⁴⁰⁻³¹³⁶=3¹⁰⁴