S=(1+2)+(2²+2³)+.....+(2⁶+2⁷)

S=   3   +2²(1+2)+....+2⁶(1+2)

S=   3   +2².3+.....+2⁶.3

S=   3(1+2²+.....+2⁶)chia hết cho 3

Tick mình đầu tiên nha

ta có 1/3^2 =1/3x3<1/2x3

          1/4^2=1/4x4<1/3x4

           ..............................

           1/21^2=1/21x21<1/20x21

suy ra ( 1/3^2+1/4^2+1/5^2+....+1/21^2)<(1/2x3+1/3x4+1/4x5+....+1/20x21)

            (1/3^2+1/4^2+1/5^2+......+1/21^2)<(1/2-1/3+1/3-1/4+1/4-1/5+.......+1/20-1/21)

             (1/3^2+1/4^2+1/5^2+.......+1/21^2)<(1/2-1/21)

              (1/3^2+1/4^2+1/5^2+.......+1/21^2)<19/42

 ta có 1/2=21/42

suy ra (1/3^2+1/4^2+1/5^2+....+1/21^2)<19/42<21/42

           (1/3^2+1/4^2+1/5^2+.....+1/21^2)<19/42<1/2

 suy ra ( 1/3^2+1/4^2+1/5^2+....+1/21^2)<1/2

            Vậy A<1/2

\(A=\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+...+\frac{1}{21^2}=\frac{1}{3.3}+\frac{1}{4.4}+\frac{1}{5.5}+...+\frac{1}{21.21}\)

\(< \frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{20.21}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{20}-\frac{1}{21}\)

\(=\frac{1}{2}-\frac{1}{21}< \frac{1}{2}\)

=> \(A< \frac{1}{2}\left(\text{ĐPCM}\right)\)

ai trả lời giúp mình

1^3+2^3+4^3+5^3=(1+2+3+4+5)^2

1³ + 2³ + 3³ + 4³ + 5³ = 1 + 8 + 27 + 64 + 125 

                                    = 225

( 1 + 2 + 3 + 4 + 5 )² = 15² = 225

\(\Rightarrow\)1³ + 2³ + 3³ + 4³ + 5³ = ( 1 + 2 + 3 + 4 + 5 )²

Hk tốt

\(1,Y=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{96}+3^{97}+3^{98}\right)\\ Y=\left(1+3+3^2\right)\left(1+3^3+...+3^{96}\right)\\ Y=13\left(1+3^3+...+3^{96}\right)⋮13\\ 2,A=\left(1+3\right)+\left(3^2+3^3\right)+...+\left(3^{2018}+3^{2019}\right)\\ A=\left(1+3\right)\left(1+3^2+...+3^{2019}\right)\\ A=4\left(1+3^2+...+3^{2019}\right)⋮4\\ 3,\Leftrightarrow2\left(x+4\right)=60\Leftrightarrow x+4=30\Leftrightarrow x=36\)

1+2+3+4+5=(1+2+3+4+5)

Ta có :

1³+2³+3³+4³+5³=1².1+2².2+3^.2.3+4².4+5².5=(1+2+3+4+5)²

........................................................................................

vay do 

231​+352​