D=4+4^2+...+4^n

=>\(4\cdot D=4^2+4^3+...+4^{n+1}\)

=>\(3D=4^{n+1}+4^n+...+4^3+4^2-4^n-...-4^2-4\)

=>\(3D=4^{n+1}-4\)

=>\(D=\dfrac{4^{n+1}-4}{3}\)

 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 
=1/(1.2)+1/(2.3)+1/(3.4)+1/(4.5) 
+1/(5.6)+1/(6.7)+1/(7.8) 
+1/(8.9)+1/(9.10) 
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5.+1/5-1/6... 
+1/9-1/10 
=1-1/10 
=9/10

1/6+1/12+1/20+1/30+1/42+1/56

=1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8

=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

=1/2-1/8

=3/8

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

\(=\frac{1}{2}-\frac{1}{8}\)

\(=\frac{3}{8}\)

a: Ta có: \(\left(2^{17}+17^2\right)\cdot\left(9^{15}-3^{15}\right)\cdot\left(2^4-4^2\right)\)

\(=\left(2^{17}+17^2\right)\cdot\left(9^{15}-3^{15}\right)\cdot\left(16-16\right)\)

=0

b: Ta có: \(\dfrac{8^{2017}-8^{2015}}{8^{2104}\cdot8}\)

\(=\dfrac{8^{2015}\cdot\left(8^2-1\right)}{8^{2105}}\)

\(=\dfrac{1\cdot63}{8^{90}}\)+

c: Ta có: \(\left(1^3+2^3+3^4+4^5\right)\cdot\left(1^3+2^3+3^3+4^3\right)\cdot\left(3^8-81^2\right)\)

\(=\left(1^3+2^3+3^4+4^5\right)\cdot\left(1^3+2^3+3^3+4^3\right)\cdot\left(3^8-3^8\right)\)

=0

d: Ta có: \(\left(2^8+8^3\right):\left(2^5\cdot2^3\right)\)

\(=\dfrac{2^8+2^9}{2^8}\)

=3

a,  2 17 + 17 2 9 15 - 3 15 2 4 - 4 2

=  2 17 + 17 2 9 15 - 3 15 16 - 16

=  2 17 + 17 2 9 15 - 3 15 . 0

= 0

b,  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 3 8 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 3 4 . 2 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 81 2 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) . 0

= 0

c,  7 24 + 7 23 : 7 22

=  7 24 : 7 22 + 7 23 : 7 22

=  7 24 - 22 + 7 23 - 22

=  7 2 + 7 1

= 49 + 7 = 56

giúp mình v mn

a, 24.( 5 - 178 ) + 178 .(10 + 24)

= 24.5 - 24 .178 + 178 .10 + 178.24

= (24.5  + 178.10)  -( 24.178 - 178.24)

=(120 + 1780) - 0

= 1900

b ,29.(-101)

= 29.( -100 -1)

= - 2900  - 29

=   -2929

c, (-56 + 130) - (43 - 56) - (-20 - 43)

    = -56 + 130 - 43 + 56 + 20 + 43

= (-56 + 56) - (43 - 43) + ( 130 + 20)

= 0 - 0 + 150

= 150 

a) ...=24×6-24.178+24.178+178×10

=144+1780=1924

b) ...=29(-100-1)=-2900-29=-2929

c) ...=-56+130-43+56+20+43=130+20=150