A= (2+2²)+(2³+2⁴)+...+(2⁹+2¹⁰)

A= 2.(1+2)+2^3.(1+2)+...2^9.(1+2)

A= 2.3+2³.3+...+2⁹.3

A= 3.(2+2³+2⁵+2⁷+2⁹)

Vậy a chia hết cho 3

A= (2+2^2)+(2^3+2^4)+(2^5+2^6)+(2^7+2^8)+(2^9+2^10)

=2.3+2^3.3+2^5.3+2^7.3+2^9.3=3(2+2^3+2^5+2^7+2^9) chia hết cho 3

A= 2+(2^2+2^3+2^4)+(2^5+2^6+2^7)+(2^8+2^9+2^10)

=2+2^2(1+2+2^2)+2^5(1+2+2^2)+2^8(1+2+2^2)=2+7(2^2+2^5+2^8) không chia hết cho 7

=> A không chia hết cho 21 

A = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ( 2⁵ + 2⁶ ) + ( 2⁷ + 2⁸ ) + ( 2⁹ + 2¹⁰ )

A = 2 . 3 + 2³ . 3 + 2⁵ . 3 + 2⁷ . 3 + 2⁹ . 3

A = 3 . ( 2 + 2³ + 2⁵ + 2⁷ + 2⁹ ) \(⋮\) 3

A = 2 + ( 2² + 2³ +2⁴ ) + ( 2⁵ + 2⁶ + 2⁷ ) + ( 2⁸ + 2⁹ + 2¹⁰ )

A = 2 + 2² . ( 1 + 2 + 2² ) + 2⁵ . ( 1 + 2 + 2² ) + 2⁸ . ( 1 + 2 + 2² )

A = 2 + 7 . ( 2² + 2⁵ + 2⁸ ) \(⋮̸\) 7

=> A \(⋮̸\) 21

hok tốt

Lần sau bạn chú ý viết đầy đủ đề.

1.

\(\sqrt{9+4\sqrt{5}-\sqrt{9-4\sqrt{5}}}=\sqrt{9+4\sqrt{5}-\sqrt{5-2\sqrt{4.5}+4}}\)

\(=\sqrt{9+4\sqrt{5}-\sqrt{(\sqrt{5}-\sqrt{4})^2}}=\sqrt{9+4\sqrt{5}-(\sqrt{5}-\sqrt{4})}\)

\(=\sqrt{9+4\sqrt{5}-\sqrt{5}+2}=\sqrt{11+3\sqrt{5}}\)

2.

\(\sqrt{8-2\sqrt{7}-\sqrt{8+2\sqrt{7}}}=\sqrt{8-2\sqrt{7}-\sqrt{7+2\sqrt{7}+1}}\)

\(=\sqrt{8-2\sqrt{7}-\sqrt{(\sqrt{7}+1)^2}}\)

\(=\sqrt{8-2\sqrt{7}-\sqrt{7}-1}=\sqrt{7-3\sqrt{7}}\)

Phạm Mạnh Kiên: sửa lại theo ý bạn thì làm như sau:

1.

\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}=\sqrt{5+2\sqrt{5}.\sqrt{4}+4}-\sqrt{5-2\sqrt{5}.\sqrt{4}+4}\)

\(=\sqrt{(\sqrt{5}+\sqrt{4})^2}-\sqrt{(\sqrt{5}-\sqrt{4})^2}=|\sqrt{5}+2|-|\sqrt{5}-2|\)

\(=\sqrt{5}+2-(\sqrt{5}-2)=4\)

2.

\(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}\)

\(=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}=|\sqrt{7}-1|-|\sqrt{7}+1|\)

\(=-2\)

\(a,\dfrac{7}{12}+\dfrac{3}{4}\times\dfrac{2}{9}=\dfrac{7}{12}+\dfrac{1}{6}=\dfrac{7}{12}+\dfrac{2}{12}=\dfrac{9}{12}=\dfrac{3}{4}\)

\(b,\dfrac{8}{9}-\dfrac{4}{15}:\dfrac{2}{5}=\dfrac{8}{9}-\dfrac{4}{15}\times\dfrac{5}{2}=\dfrac{8}{9}-\dfrac{2}{3}=\dfrac{8}{9}-\dfrac{6}{9}=\dfrac{2}{9}\)

đùa thì kệ con mẹ mày xàm loz

Đáp án a là 0,75 

Đáp án b: là 0.86222222222

A = ( 2+2²+2³) + (2⁴+2⁵+2⁶) + (2⁷+2⁸+2⁹)+  (2¹⁰+2¹¹+2¹²)

A = 2.(1+2+2²) +2⁴.(1+2+2²) +2⁷.(1+2+2²)+ 2¹⁰.(1+2+2²)

A = 2.7+2⁴.7 +2⁷.7+ 2¹⁰.7

A = 7.( 2+2⁴+2⁷+2¹⁰)

Suy ra A chia hết cho 7

A=2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2¹⁰+2¹¹+2¹²

=2(1+2+2²)+2⁴(1+2+2²)+2⁷(1+2+2²)+2¹⁰(1+2+2²)

=2.7+2.7+2.7+2.7

Vậy A chia hết cho 7

có:

(1994-1)+1=1994

Tổng là:

1994x(1994+1):2=1989015

Đáp số:1989015