a/

\(A=3^2+3^2.2^2+3^2.3^2+3^2.4^2+...+3^2.30^2=\)

\(=3^2\left(1^2+2^2+3^2+...+30^2\right)\)

Đăt biểu thức trong dấu ngoặc là B

\(B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+30\left(31-1\right)=\)

\(=1.2+2.3+3.4+30.31-\left(1+2+3+...+30\right)=\)

\(C=1+2+3+...+30=\dfrac{30\left(1+30\right)}{2}=465\)

\(D=1.2+2.3+3.4+...+30.31\)

\(3D=1.2.3+2.3.3+3.4.3+...+30.31.3=\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+30.31.\left(32-29\right)=\)

\(=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-29.30.31+30.31.32=\)

\(=30.31.32\Rightarrow D=\dfrac{30.31.32}{3}=10.31.32\)

\(\Rightarrow A=3^2\left(C-D\right)=3^2\left(10.31.32-465\right)\)

b/

Đặt biểu thức là A

\(\dfrac{A}{2}=\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+\dfrac{9-7}{7.9}+...+\dfrac{39-37}{37.39}=\)

\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{37}-\dfrac{1}{39}=\)

\(=\dfrac{1}{3}-\dfrac{1}{39}=\dfrac{12}{39}\Rightarrow A=\dfrac{2.12}{39}=\dfrac{24}{39}=\dfrac{8}{13}\)

\(A=3.3+6.6+9.9+...+90.90\)

\(A=3^2\left(1+2^2+3^2+...+10^2\right)\)

\(A=9.\dfrac{10.\left(10+1\right)\left(2.10+1\right)}{6}\)

\(A=3.\dfrac{10.11.21}{2}\)

\(A=3465\)

bằng 49,5 nhé bạn

đúng rồi duyệt đi

ta có :

\(\frac{1}{3^2}< \frac{1}{2.3}\)

\(\frac{1}{4^2}< \frac{1}{3.4}\)

......................

\(\frac{1}{100^2}< \frac{1}{99.100}\)

\(\Leftrightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(\Leftrightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Leftrightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{2}-\frac{1}{100}\)

\(\Leftrightarrow\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{49}{100}< \frac{1}{2}\)

                                                                                                                      HC TỐT NHÉ ( NHỚ K CHO MK NHA , MỎI TAY LẮM ĐÓ )

@Ayawasa Misaki sai đề kìa

Đang kiếm người để k  :)))))

1,1

2,4

3,9

4,16

5,25

6,36

7,49

8,64

9,81

10,-1711

Học tốt

1.1=1

2.2=4

3.3=9

4.4=16

5.5=25

6.6=36

7.7=49

8.8=64

9.9=81

54+69-12.71+58-65.32:2=-1711

25

36

49

64

81

100

tk mk với nha.mk xin đó

Mấy bn tk cho mk ik .rồi mk cho mỗi người 3 tk

5.5=25

6.6=36

7.7=49

8.8=64

9.9=81

10.10=100

#Học tốt