a)Đặt \(A=\dfrac{6}{1.4}+\dfrac{6}{4.7}+\dfrac{6}{7.10}+...+\dfrac{6}{97.100}\)

\(3a=3-\dfrac{3}{4}+\dfrac{3}{4}-\dfrac{3}{7}+\dfrac{3}{7}-\dfrac{3}{10}+...+\dfrac{3}{97}-\dfrac{3}{100}\)

\(=3-\dfrac{3}{100}\)

\(=\dfrac{297}{100}\)

b)Đặt \(B=\dfrac{4}{1.3}+\dfrac{16}{3.5}+\dfrac{36}{5.7}+...+\dfrac{9604}{97.99}\)

\(=2b=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\)

\(2b=2-\dfrac{2}{3}+\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{5}-\dfrac{2}{7}+...+\dfrac{2}{97}-\dfrac{2}{99}\)

\(2b=2-\dfrac{2}{99}=\dfrac{198}{99}-\dfrac{2}{99}=\dfrac{196}{99}\)

c) Tương tự! Bạn tự làm nhé!

Kết quả là:

 161651

  Đpá số: 161651

161651

ban nhe

tk nha@@@@@@@@@@@@@@@@@@@@@@@@2

hihi

\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{3}{5.7}+...+\dfrac{4}{97.99}\)
\(=2\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{97.99}\right)\)
\(=2\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(=2\left(1-\dfrac{1}{99}\right)\)
\(=2\cdot\dfrac{98}{99}\)
\(=\dfrac{196}{99}\)
#NoSimp

=2(2/1*3+2/3*5+...+2/97*99)

=2(1-1/3+1/3-1/5+...+1/97-1/99)

=2*98/99=196/99

\(\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+...+\dfrac{4}{97.99}\)

=4.(\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)

=4.1/2.(2/1.3+2/3.5+2/5.7+...+2/97.99)

=2.(1/1-1/3+1/3-1/5+1/5-1/7+...+1/97-1/99)

=2.(1/1-1/99)

=2.(99/99-1/99)

=2.98/99

=196/99

Khoảng cách giữa hai thừa số trong mỗi số hạng là 2, nhân 2 vế của A với 3 lần khoảng cách này ta được :

6A=1.3.6 + 3.5.6 + 5.7.6 + ... + 97.99.6

=1.3(5+1) + 3.5(7-1) + 5.7(9-3) + ... + 97.99(101-95)

=1.3.5 + 1.3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99

=1.3.5 + 3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7+ ... + 97.99.101 - 97.97.99

=3+97.99.101

\(\frac{1+97.33.101}{1}=161651\)

Ta có :

B = 1.3 + 3.5 + 5.7 + 7.9 + ... + 97.99

6.B = 1.3.6 + 3.5.6 + 5.7.6 +...+ 97.99.6

6.B = 1.3.[ 5 - (-1) ] + 3.5.( 7 - 1 ) + 5.7.( 9 - 3 ) + ...+ 97.99.( 101 - 95 )

6.B = 1.3.5 - ( -1).3.5 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99

6.B = 97.99.101 - ( -1 ) .3.5

6.B = 97.99.101 + 1.3.5

6.B = 969918

=> B = 161653.

Ta có :
B = 1.3 + 3.5 + 5.7 + 7.9 + ... + 97.99
6.B = 1.3.6 + 3.5.6 + 5.7.6 +...+ 97.99.6
6.B = 1.3.[ 5 - (-1) ] + 3.5.( 7 - 1 ) + 5.7.( 9 - 3 ) + ...+ 97.99.( 101 - 95 )
6.B = 1.3.5 - ( -1).3.5 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99
6.B = 97.99.101 - ( -1 ) .3.5
6.B = 97.99.101 + 1.3.5

6.B = 969918
=> B = 16165

k cho mk nha Trần Thế Khoa đẹp trai