Question

Tính M=3⁶-(3⁵+3⁴+...+3¹+3⁰)

Answer 1

Lời giải:

$3^6-M=3^0+3^1+3^2+3^3+3^4+3^5$

$3(3^6-M)=3^1+3^2+3^3+3^4+3^5+3^6$

$\Rightarrow 3(3^6-M)-(3^6-M)=3^6-3^0$

$\Rightarrow 2(3^6-M)=3^6-1$

$\Rightarrow 2M = 2.3^6-(3^6-1)=3^6+1$

$\Rightarrow M=\frac{3^6+1}{2}$

Answer 2

M=36-(35+34+...+31+30)

   Đặt A=35+34+...+31+30

        3A=3⁶+3⁵+...+3²+31

        3A-A=3⁶+3⁵+...+3²+31-35-34-...-31-30

        2A=3⁶-30=>A=\(\dfrac{3^6-3^0}{2}\)

 Thay A vào M ta có:

M=3⁶-\(\dfrac{3^6-3^0}{2}\)

M=\(\dfrac{2.3^6}{2}\)-\(\dfrac{3^6-3^0}{2}\)

M=\(\dfrac{3^6.\left(2-1\right)-1}{2}\)

M=\(\dfrac{3^6.1-1}{2}\)

M=\(\dfrac{3^6-1}{2}\)

M=364