Ta đặt tên cho biểu thức này là : A

 => A = 2 + 2^2 + 2^3 + ... + 2^60

=> 2A = 2. ( 2 + 2^2 + 2^3 + ... + 2^60 )

 => 2A =  2^2 + 2^3 + 2^4 + ...+ 2^61

=>  2A - A = 2^2 + 2^3 + 2^4 + ... +2^61 - 2 - 2^2 - 2^3 - ...- 2^60

=>        A   =            2^61 - 2

Đặt A = 2 + 2² + 2³ +...+ 2⁶⁰ 

\(\Rightarrow\)2A = 2² + 2³ + 2⁴ +...+ 2⁶¹ 

\(\Rightarrow\)2A - A = ( 2² + 2³ + 2⁴ +...+ 2⁶¹ ) - ( 2 + 2² + 2³ +...+ 2⁶⁰ )

\(\Rightarrow\)A = 2⁶¹ - 2

         ~ Hok tốt ~

         A=   2+2²+2³+...+2⁶⁰

         2 . A = 2 . ( 2 + 2² + 2³ + ...+2⁶⁰)

         2. A =  2 . 2 + 2. 2²+2.2³ + ...+ 2.2⁶⁰

         2 .A =   2²   +  2³   + 2⁴ + ... +  2⁶¹

         2A - A = (  2^2₊2³ + ...+ 2⁶¹) - ( 2+ 2²+2³+2⁴+...+2⁶⁰)

           A       = 3⁶¹ - 2 

            k m nha

\(=\left(95^2-2\cdot60\cdot95+60^2\right)-30^2\\ =\left(95-60\right)^2-30^2=35^2-30^2=\left(35-30\right)\left(35+30\right)\\ =5\cdot65=325\)

\(S=6^2\left(1^2+2^2+3^2+...+10^2\right)=36.385=13860\)

13860 mình cùng lớp bạn đấy đó bạn biết là ai:))_

Đặt A = 1+2+2^2+2^3+....+2^60

2A = 2+2^2+2^3+2^4+.....+2^61

2A-A= ( 2+2^2+2^3+....+2^61)-(1+2+2^2+.....+2^60)

A = 2^61-1

http://olm.vn/hoi-dap/question/232902.html

2A = 2 + 2^2 + 2^3 + 2^4 +...+ 2^61

=> A = ( 2 + 2^2 + 2^3 + 2^4 +...+ 2^61 ) - ( 1 + 2 + 2^2 + 2^3 +...+ 2^60 )

=> A = 2^61 - 1

cho minh nhé

A=(2+2^2)+...+(2^59+2^60) 
A=2(1+2)+...+2^59(1+2) 
A=3(2+2^3+...+2^59) 
nên A chia hết cho 3. 
A= (2+2^2+2^3)+...+(2^58+2^59+2^60) 
A=2(1+2+2^2)+...+2^58(1+2+2^2) 
A=7(2+2^4+..+2^58) 
nên A chia hết cho 7 
A= (2+2^2+2^3+2^4)+....+(2^57+2^58+2^59+2^6... 
=2(1+2+2^2+2^3)+....+2^57(1+2+2^2+2^3)... 
=15(2+2^5+...+2^57) 
nên A chia hết cho 15

A = 2 + 2² + 2³ +... + 2⁶⁰

  = ( 2 + 2² ) + ( 2³ + 2⁴ ) +... + ( 2⁵⁹ + 2⁶⁰ )

  = 2. ( 1 + 2 ) + 2³. ( 1 + 2 ) +... + 2⁵⁹. ( 1 + 2 )

 = 2.3 + 2³ .3 + .... + 2⁵⁹.3

  = ( 2 + 2³ +... + 2⁵⁹ ) . 3 chia hết cho 3

=> A chia hết cho 3

A = 2 + 2² + 2³ +... + 2⁶⁰

    = ( 2 + 2² + 2³ + 2⁴ ) +... + ( 2⁵⁷ + 2⁵⁸ + 2⁵⁹ + 2⁶⁰ )

   = 2. ( 1 + 2 + 2² + 2³ ) +... + 2⁵⁷. ( 1 + 2 + 2² + 2³ )

   = 2. 15 +...... + 2⁵⁷. 15

   = ( 2 + ..... + 2⁵⁷ ) . 15         chia hết cho 15

=> A chia hết cho 15

A CHIA HẾT CHO 15

S=1+2+2^2+2^3+2^4+2^5+2^6+...+2^60

S = 2⁶¹-1

\(S=\left(2-1\right)\left(1+2+2^2+...+2^{60}\right)\)

\(=2^{61}-1\)

S = 1 + 2 + 2² + 2³ + ... + 2⁶⁰

2S = 2 + 2² + 2³ + 2⁴ + ... + 2⁶¹

2S - S = (2 + 2² + 2³ + 2⁴ + ... + 2⁶¹) - (1 + 2 + 2² + 2³ + ... + 2⁶⁰)

S = 2⁶¹ - 1

\(\left(a-b\right)^2=a^2+b^2-2ab\\ \Rightarrow49=a^2+b^2-120\Rightarrow a^2+b^2=169\)

\(\left(a+b\right)^2=a^2+b^2+2ab=169+120=289\\ \Rightarrow a+b=17\)

\(a^2-b^2=\left(a-b\right)\left(a+b\right)=7\cdot17=119\)

\(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=169^2-2\cdot60^2\\ =28561-7200=21361\)

\(2\left(x^2+y^2\right)=\left(x-y\right)^2\\ \Rightarrow2x^2+2y^2=x^2-2xy+y^2\\ \Rightarrow x^2+2xy+y^2=0\\ \Rightarrow\left(x+y\right)^2=0\Rightarrow x+y=0\Rightarrow x=-y\)

\(\dfrac{2}{20}-\dfrac{-3}{36}+\dfrac{4}{60}=\dfrac{1}{4}\)

=\(\dfrac{1}{4}\)

\(\dfrac{2}{20}-\left(-\dfrac{3}{36}\right)+\dfrac{4}{60}\\ =\dfrac{1}{10}+\dfrac{1}{12}+\dfrac{1}{15}\\ =\dfrac{6}{60}+\dfrac{5}{60}+\dfrac{4}{60}\\ =\dfrac{6+5+4}{60}\\ =\dfrac{15}{60}\\ =\dfrac{1}{4}\)