N=\(3.\left(\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{197.199}\right)\)

N=\(\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{197.199}\right)\)

N=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right)\)

N=\(\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{999}\right)\)

N=\(\frac{3}{2}.\frac{194}{995}\)

N=\(\frac{291}{995}\)

= 3/5-3/7+3/7-3/9+3/9-3/11+......+3/197-3/199

= 3/5-3/199

= 582/995

\(N=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{197}-\frac{1}{199}\right)\)

\(N=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{199}\right)\)

\(N=\frac{3}{2}\cdot\frac{194}{995}\)

\(N=\frac{291}{995}\)

N=3/2(1/5-1/7+1/7-1/9+1/9-1/11+...+1/197-1/199)

N=3/2(1/5-1/199)=3/2.194/995=291/995

\(\frac{2}{3}N=\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+...+\frac{1}{197.199}\)

          \(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{197}-\frac{1}{199}\)

          \(=\frac{1}{5}-\frac{1}{199}\) 

          \(=\frac{194}{995}\)

=> \(N=\frac{194}{995}:\frac{2}{3}=\frac{291}{995}\)

=> 2N = 2.3/5.7 + 2.3/7.9 + 2.3/9.11 + ... + 2.3/197.199

=> 2N = 3. (1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11   + ... + 1/197 - 1/199

=> 2N = 3. (1/5 - 1/199) = 3. 194/995 = 582/995

=> N = 582/995 : 2 = 291/995

Tinh bang mt do nha.

N=3/5.7+3/7.9+3/9.11+..................+3/197.199

N=1/5-1/7+1/7-1/9+...........+1/197.199

N=1/5-1/199

=194/995

BAIF 2

=2/3.5+2/5.7+...........+2/97.99

=2/3-2/5+2/5-2/7+............2/97-2/99

=1/3-1/5=1/5-1/7+............+1/97-1/99

=1/3-1/99

=32/99

a.  

\(M=1.\left[\frac{1}{3}-\frac{1}{5}+.....\frac{1}{97}-\frac{1}{99}\right]\)

\(M=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)

b.

\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right]\)

\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{199}\right]=\frac{291}{995}\)

mk đầu tiên nha bạn

N=3/2.(1/5.7+1/7.9+1/9.11+....+1/197.199)

N=3/2.(1/5-1/7+1/7-1/9+1/9-1/11+....+1/197-1/199)

N=3/2.(1/5-1/199)

N=3/2.194/995

N=291/995

Có N = 3 . (1/5 .  7 + 1/7 . 9 + .... + 1/197 . 199)

    2N =  3 . (2/5 . 7 + 2/7 . 9 + ... + 2/197 . 199)

    2N = 3 . (1/5 - 1/7 + 1/7 - 1/9 + ... + 1/197 - 1/199)

    2N = 3 . (1/5 - 1/199)

      N = \(\frac{3.\left(\frac{1}{5}-\frac{1}{199}\right)}{2}\)

      N = (3 . 194/995) : 2

Bạn tự tính nốt nhé chúc bạn học tốt

biểu thức trên =\(\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{56}-\frac{1}{61}\right)=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{1}{2}x\frac{61}{305}=\frac{1}{10}=0,1.\)

vậy biểu thức trên =0,1

a)\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\cdot\frac{402}{2015}\)

\(=\frac{603}{2015}\)

b)\(=\frac{4}{5}\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{8}-\frac{1}{13}+...+\frac{1}{93}-\frac{1}{98}\right)\)

\(=\frac{4}{5}\left(\frac{1}{3}-\frac{1}{98}\right)\)

\(=\frac{4}{5}\cdot\frac{95}{294}\)

\(=\frac{38}{147}\)

a) Gọi tổng trên là A

A = \(\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{2013.2015}\)

A == \(\frac{3}{5}-\frac{3}{7}+\frac{3}{7}-\frac{3}{9}+\frac{3}{9}-\frac{3}{11}+...+\frac{3}{2013}-\frac{3}{2015}\)

Vì một số trừ cho a rồi cộng cho a sẽ bằng chính số đó nên:

A = \(\frac{3}{5}-\frac{3}{2015}\)

A = \(\frac{1209}{2015}-\frac{3}{2015}\)

A = \(\frac{1206}{2015}\)

b) Gọi tổng trên là B

B = \(\frac{4}{3.8}+\frac{4}{8.13}+\frac{4}{13.15}+...+\frac{4}{93.98}\)

B = \(\frac{4}{3}-\frac{4}{8}+\frac{4}{8}-\frac{4}{13}+\frac{4}{13}-\frac{4}{15}+...+\frac{4}{93}-\frac{4}{98}\)

Vì một số trừ cho a rồi cộng cho a sẽ bằng chính số đó nên:

B = \(\frac{4}{3}-\frac{4}{98}\)

B = \(\frac{686}{294}-\frac{12}{294}\)

B = \(\frac{674}{294}=\frac{337}{147}\)

bai thang dung roi

2\3x-780\11:[13\2.(1\3.5+1\5.7+1\7.9+1\9.11]=-5

2\3x-780\11:[13\2.(1\3-1\5+1\5-1\7+....+1\9-1\11)]=-5

2\3x-780\11:[13\2.(1\3-1\11)]=-5

2\3x-780\11:[13\2.8\33]=-5

2\3x-780\11:52\33=-5

2\3x-525\13=-5

2\3x=-5+525\13

2\3x=460\13

x=460\13:2\3

x=690\13