Bài tập 64 trang 18 SBT Toán 6 Tập 2

Chứng tỏ rằng :

\(\dfrac{1}{2^2}\) + \(\dfrac{1}{3^2} \) + ... + \(\dfrac{1}{100^2}\) < 1

Cho minh hoi bai nay vs:

Chung to S=\(\dfrac{1}{4}\)+\(\dfrac{2}{4}\)+...+\(\dfrac{10}{4}\)<14

Chung to S=\(\dfrac{1}{6}+\dfrac{1}{7}+...+\dfrac{1}{19}< 2\)

Chung to S=\(\dfrac{1}{10}+\dfrac{1}{4}+...+\dfrac{1}{100}>1\)

CMR :

\(A=\dfrac{1}{3}+\dfrac{1}{4}+....+\dfrac{1}{32}>2\)

E đg cần gấp lắm ạ; Mong mấy ah cj ; giải dùm ạ !!!!!!!!!!

Mơn

1) Tính

a)\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{99.101}\)

b)\(\dfrac{1}{4}+\dfrac{1}{32}+\dfrac{1}{96}+\dfrac{1}{192}\)(Điều kiện: không quy đồng và máy tính bỏ túi)

Tính 2/3.5+2/5.7+2/7.9+...+2/97.99

Tính tổng

A=1/1.2+1/2.3+.......+1/49/50

B=2/3.5+2/5.7+..........+2/37.39

C=3/4.7+3/7.10+.........+3/37.39

Ai giúp mình với!!!!!!!!!!!!!!!!!!!!!!!!!!!

Tìm số nguyên x, biết:

\(\dfrac{x}{6}+\dfrac{x}{10}+\dfrac{x}{15}+\dfrac{x}{21}+\dfrac{x}{28}+\dfrac{x}{36}+\dfrac{x}{45}+\dfrac{x}{55}+\dfrac{x}{66}+\dfrac{x}{78}=\dfrac{200}{39}\)

1, Chứng minh

a) A=\(\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+\dfrac{1}{3.4.5}+....+\dfrac{1}{18.19.20}< \dfrac{1}{4}\)

b) B=\(\dfrac{36}{1.3.5}+\dfrac{36}{3.5.7}+\dfrac{36}{5.7.9}+....+\dfrac{36}{25.26.27}< 3\)

1. tìm x thuộc z biết \(\dfrac{x}{-12}\)=\(\dfrac{-3}{2}\)

2 tính

a,\(\dfrac{-7}{9}\times\dfrac{6}{11}+\dfrac{-2}{9}\)

b,\(\dfrac{-4}{7}:2=\)

c,115- (24-5\(\times\)3)

d,\(\dfrac{-3}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{-3}{7}+2\dfrac{3}{7}\)

e,\(\dfrac{1}{4\times5}+\dfrac{1}{6\times7}+......\dfrac{1}{79\times80}\)

1/5+-1/6+1/7+-1/8+1/9+1/8+-1/7+1/6+-1/5

\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{\left(2x-2\right).2x}=\dfrac{11}{48}\left(x\in N;x\ge12\right)\)

S = \(\dfrac{1}{1.2}\) +...+ \(\dfrac{1}{49.50}\)

S = \(\dfrac{3}{1.4}\) + \(\dfrac{3}{4.7}\) + ... + \(\dfrac{3}{43.46}\)

S = \(\dfrac{1}{15}\) + \(\dfrac{1}{35}\) + ... + \(\dfrac{1}{2499}\)

S = \(\dfrac{1}{123}\) + \(\dfrac{1}{234}\) + ... + \(\dfrac{1}{9899100}\)

\(\dfrac{1}{3}\)+\(\dfrac{1}{3^2}\)+\(\dfrac{1}{3^3}\)+....+\(\dfrac{1}{3^{2016}}\)

Tìm x€Z: 1/3 + 1/6 + 1/1 +...+ 2/x.(x+1)=1999/2001

Tính nhanh:

\(M=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{995.997}+\dfrac{1}{997.999}\)

Thực hiện phép tính sau:

M=\(\dfrac{20}{112}+\dfrac{20}{280}+\dfrac{20}{520}+\dfrac{20}{832}\)

Chứng Minh Rằng :

\(\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+...+\dfrac{1}{100^2}>\dfrac{1}{5}\)

(giúp mình nha!)

Tính

A= \(\dfrac{3^2}{8.11}\)+ \(\dfrac{3^2}{18.21}\)+ \(\dfrac{3^2}{14.17}\)+......+ \(\dfrac{3^2}{197.200}\)

B= \(\dfrac{1}{25.27}\)+ \(\dfrac{1}{27.29}\)+ \(\dfrac{1}{29.31}\)+....+ \(\dfrac{1}{73.75}\)

các bạn giải ra giúp mik nha ! Thanks

1.Tính giá trị biểu thức sau:

A=\(\dfrac{2}{2.5}\)\(+\)\(\dfrac{2}{5.8}\)\(+\)\(\dfrac{2}{8.11}\)\(+\)...........\(+\)\(\dfrac{2}{92.95}\)\(+\)\(\dfrac{2}{95.98}\)

Giúp mình nha các cậu

Tính 4/6.8+4/8.10+...+4/40.42

\(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}+\dfrac{2}{39}\)

tính

Cho A=\(\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{50^2}\)

Chứng minh A<2

tính

A= 1+ \(\dfrac{1}{2}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{8}\) + ......+ \(\dfrac{1}{1024}\) giúp mk Quỳnh Phương Nguyễn Ace Legona Nguyễn Huy Tú

Tính S=1+1/2+1/2^2+....+1/2^2006

Chứng minh 1/2^2+1/3^2+1/4^2+...+1/8^2 < 1-1/8

15/90.94 + 15/94.98 + 15/98.102 +...+15/146.150

\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{\left(2x-2\right).2x}=\dfrac{11}{48}\left(x\in N;x\ge12\right)\)

Bài 2 : Cho S = \(\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}+\dfrac{3}{14}+\dfrac{3}{15}\)

Chứng tỏ 1<S<2