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\(C=1+\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{18}}=1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{8}+...+\dfrac{1}{131072}-\dfrac{1}{262144}=1+1-\dfrac{1}{262144}=2-\dfrac{1}{262144}\)

810 - 89 - 88 = 88 . 82 - 88 . 8 - 88 = 88(82 - 8 - 1 ) = 88 . 55 chia hết cho 55


2.
\(\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot15\cdot37\right)\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left(65\cdot111-13\cdot5\cdot3\cdot37\right)\\=\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-\left(13\cdot5\right)\cdot\left(3\cdot37\right)\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot\left[65\cdot111-65\cdot111\right]\\ =\left(1+2+3+...+100\right)\cdot\left(1^2+2^2+3^2+...+10^2\right)\cdot0\\ =0\)

a) {[( 32 + 1 ) . 10 - ( 8 : 2 + 6 ) ] : 2 } + 55 -( 10 : 5 )3
= ( 10 . 10 - 10 : 2 ) + 55 - 6
= 90 : 2 ) + 55 - 6
= 45 + 55 - 6
= 100 - 6
= 94
b) 100 - [ 60 - ( 9 - 2 )2 ] . 32
= 100 - [ 60 - 72 ] . 9
= 100 - [ 60 - 49 ] . 9
= 100 - 11 . 9
= 100 - 99
= 1
c) [ ( 1253 ) . 75 - ( 175 )5 : 5 ] : 20162017
= 0 : 20162017
= 0
+ bài d kg hiểu! Xin lỗi

A=1+2+22+23+....+210
=> 2A=2(1+2+22+23+....+210)
=> 2A=2+22+23+24+....+211
=> 2A-A=211-1
*) B=1+3+32+33+....+3100
=> 3B=3+32+33+34+....+3101
=> 2B=3101-1
=> B=\(\frac{3^{101}-1}{2}\)
2A= 2 + 22 + 24 + 25 + 26 + 27 + 28 +29 + 210 + 211
Lay 2A- A = (2 + 22 + 24 + 25 + 26 + 27 + 28 +29 + 210 + 211) - ( 1 + 2 + 22 + 24 + 25 + 26 + 27 + 28 +29 + 210)
A = 211-1
3B = 3 + 32 + 33 + 34 + 35 + ... + 3101
Lay 3B - B = (3 + 32 + 33 + 34 + 35 + ... + 3101) - ( 1 + 3 + 32 + 33 + 34 + ... + 3100)
2B = 3101-1
B = (3101-1)/ 2