`A=2^{0}+2^{1}+2^{2}+....+2^{99}`

`=(1+2+2^{2}+2^{3}+2^{4})+(2^{5}+2^{6}+2^{7}+2^{8}+2^{9})+......+(2^{95}+2^{96}+2^{97}+2^{97}+2^{99})`

`=(1+2+2^{2}+2^{3}+2^{4})+2^{5}(1+2+2^{2}+2^{3}+2^{4})+.....+2^{95}(1+2+2^{2}+2^{3}+2^{4})`

`=31+2^{5}.31+....+2^{95}.31`

`=31(1+2^{5}+....+2^{95})\vdots 31`

\(A=2^0+2^1+2^2+2^3+2^4+2^5+2^6+...+2^{99}\)

\(=\left(2^0+2^1+2^2+2^3+2^4\right)+2^5\left(2^0+2^1+2^2+2^3+2^4\right)+...+2^{95}\left(2^0+2^1+2^2+2^3+2^4\right)=31+31.2^5+...+31.2^{95}=31\left(1+2^5+...+2^{95}\right)⋮31\)

A = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ … + 2⁹⁹

^A=( 2⁰ + 2¹ + 2² + 2³ + 2⁴⁾ +( 2⁵ … + 2⁹⁹⁾

A= 2⁰.(2⁰ + 2¹ + 2² + 2³ + 2⁴)+2⁵.( 2⁵ … + 2⁹⁹⁾

A= 1. 31+ 2⁵.31… + 2⁹⁵.31

^A= 31. (1+2⁵...+2⁹⁵)

KL: ...... 

\(A=2^0+2^1+2^2+2^3+2^4+...+2^{99}=\left(2^0+2^1+2^2+2^3+2^4\right)+2^5\left(2^0+2^1+2^2+2^3+2^4\right)+...+2^{95}\left(2^0+2^1+2^2+2^3+2^4\right)=31+31.2^5+...+31.2^{95}=31\left(1+2^5+...+2^{95}\right)⋮31\)

A = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ … + 2⁹⁹

A=( 2⁰ + 2¹ + 2² + 2³ + 2⁴⁾ +( 2⁵ … + 2⁹⁹⁾

A= 2⁰.(2⁰ + 2¹ + 2² + 2³ + 2⁴)+2⁵.( 2⁵ … + 2⁹⁹⁾

A= 1. 31+ 2⁵.31… + 2⁹⁵.31

A= 31. (1+2⁵...+2⁹⁵)

KL: ...... 

1/

Tổng A là tổng các số hạng cách đều nhau 4 đơn vị.

Số số hạng: $(101-1):4+1=26$

$A=(101+1)\times 26:2=1326$

2/

$B=(1+2+2^2)+(2^3+2^4+2^5)+(2^6+2^7+2^8)+(2^9+2^{10}+2^{11})$

$=(1+2+2^2)+2^3(1+2+2^2)+2^6(1+2+2^2)+2^9(1+2+2^2)$

$=(1+2+2^2)(1+2^3+2^6+2^9)$

$=7(1+2^3+2^6+2^9)\vdots 7$

3/
$C=1+2+2^2+2^3+...+2^{99}$

$2C=2+2^2+2^3+2^4+...+2^{100}$

$\Rightarrow 2C-C=2^{100}-1$

$\Rightarrow C=2^{100}-1$

a: \(\left[600-\left(40:2^3+3\cdot5^3\right)\right]:5\)

\(=\left[600-5-375\right]:5\)

\(=44\)

b: \(16\cdot12^2-\left(4\cdot23^2-59\cdot4\right)\)

\(=16\cdot144-4\cdot\left(23^2-59\right)\)

\(=2304-4\cdot470\)

\(=424\)

c: Ta có: \(2^{100}-\left(1+2+2^2+2^3+...+2^{99}\right)\)

\(=2^{100}-2^{100}+1\)

=1

d: Ta có: \(169\cdot2011^0-17\cdot\left(83-1702:23+1^{2012}\right)+2^7:2^4\)

\(=169-17\cdot\left(83-74+1\right)+2^3\)

\(=177-17\cdot10\)

=7

Số số hạng của dãy trên là: (30-20):1+1 = 11 (số)

Tổng trên là: (30+20) x 11:2 = 275

                 Đáp số: 275

=(20+30)+...(24+26)+25

=50+50+50+50+25

=50x4+25

=225

20+21+22+23+24+25+26+27+28+29+30

=(20+30)+(21+29)+(22+28)+(23+27)+(24+26)+25

=50+50+50+50+50+25

=250+25

=275

Ủng hộ mk nkoa!^_^

Trả lời :

20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 = 188

~ Học tốt ~

Gộp lại thôi

a. = 6.

\(A=2+2^3+...+2^{101}\)

\(4A=2^3+2^5+...+2^{101}+2^{103}\)

\(4A-A=2^{103}-2\)

\(3A=2^{103}-2\)

\(A=\dfrac{2^{103}-2}{3}\)

\(\Rightarrow1+2+2^3+...+2^{101}=A+1=\dfrac{2^{103}+1}{3}\)

\(20+21+22+23+24+25+26+27+28+29+30=275\)

(Nhớ k cho mình với nhé!)

cach tinh nhanh 

20+21+22+23+24+25+26+27+28+29+30=275

=(29+20)x5=49x5=245

tick đúng nha

ta thay 21+29=50

co 4 cap =50 

số ở giữa là

[29+21];2=25

tổng là 20+50x4+25=245