a, A là   cộng theo số lẻ ( 1 + 3 = 4 ,4 + 5 = 9.....) bắt đầu từ 3 

b , B là mỗi lần cộng thêm 6 

c , A là cộng theo số lẻ ( 1 + 3 = 4 ,4 + 5 = 9.....)

d, B là cộng theo số chẵn bắt đầu từ 4 

hok tốt

\(\dfrac{1}{10}+\dfrac{4}{20}+\dfrac{9}{30}+\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)
\(=\dfrac{1}{10}+\dfrac{1}{5}+\dfrac{3}{10}+\dfrac{2}{5}+\dfrac{1}{2}+\dfrac{3}{5}+\dfrac{7}{10}+\dfrac{4}{5}+\dfrac{9}{10}\)
\(=\left(\dfrac{1}{10}+\dfrac{3}{10}+\dfrac{7}{10}+\dfrac{9}{10}\right)+\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{3}{5}+\dfrac{4}{5}\right)+\dfrac{1}{2}\)
\(=2+2+\dfrac{1}{2}\)
\(=4+\dfrac{1}{2}\)
\(=\dfrac{8}{2}+\dfrac{1}{2}=\dfrac{9}{2}\)

D

Chọn D

1=1x1

4=2x2

9=3x3...

36=6x6

49=7x7

64=8x8

Chọn A

A

A

A=1/2²+1/3²+...+1/9²

Ta có:1/2²>1/2.3,1/3²>1/3.4,...,1/9²>1/9.10

⇒A>1/2.3+1/3.4+...+1/9.10

A>1/2-1/3+1/3-1/4+...+1/9-1/10

A>1/2-1/10

A>2/5(đpcm)

Ta có: A = 1/4 + 1/9 + 1/16 + 1/25 +1/36 + 1/49 + 1/64 + 1/81

Vì 1/2²>1/2.3,1/3²>1/3.4,...,1/9²>1/9.10

=>A>1/2.3+1/3.4+...+1/9.10

=>A>1/2-1/3+1/3-1/4+...+1/9-1/10

=>A>1/2-1/10

=>A>2/5

Giải:

\(A=\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\dfrac{1}{25}+\dfrac{1}{36}+\dfrac{1}{49}+\dfrac{1}{64}+\dfrac{1}{81}\) 

\(A=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2} +\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}+\dfrac{1}{9^2}\) 

Ta có:

\(\dfrac{1}{2^2}=\dfrac{1}{2.2}>\dfrac{1}{2.3}\) 

\(\dfrac{1}{3^2}=\dfrac{1}{3.3}>\dfrac{1}{3.4}\) 

\(\dfrac{1}{4^2}=\dfrac{1}{4.4}>\dfrac{1}{4.5}\) 

\(\dfrac{1}{5^2}=\dfrac{1}{5.5}>\dfrac{1}{5.6}\) 

\(\dfrac{1}{6^2}=\dfrac{1}{6.6}>\dfrac{1}{6.7}\) 

\(\dfrac{1}{7^2}=\dfrac{1}{7.7}>\dfrac{1}{7.8}\) 

\(\dfrac{1}{8^2}=\dfrac{1}{8.8}>\dfrac{1}{8.9}\) 

\(\dfrac{1}{9^2}=\dfrac{1}{9.9}>\dfrac{1}{9.10}\) 

\(\Rightarrow A>\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\) 

\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(\Rightarrow A>\dfrac{1}{2}-\dfrac{1}{10}\) 

\(\Rightarrow A>\dfrac{2}{5}\left(đpcm\right)\) 

Chúc bạn học tốt!

bấm máy tính đi bạn, nhanh hơn

ĐÂY LÀ TÍNH NHANH

theo đề bài ra ta có:1+4+9+16+25+36+49+64+81+100

=(1+49)+(4+16)+(9+81)+(36+64)+(25+100)

=50+20+100+100+125

=70+100+100+125

=170+100+125

=270+125

=395

Có tính nhanh ko?

\(1=1^2;4=2^2;9=3^2;16=4^2;25=5^2\)\(36=6^2;49=7^2;64=8^2;81=9^2;100=10^2\)

\(1=1^2\)                                                       \(36=36^2\)

\(4=4^2\)                                                       \(49=49^2\)

\(9=9^2\)                                                        \(64=64^2\)

\(16=16^2\)                                                   \(81=81^2\)

\(25=25^2\)                                                    \(100=100^2\)

1= 1^2                    4=2^2              9=3^2             16=4^2          25=5^2             36=6^2              49=7^2          64=8^2

81=9^2               100=10^2