\(F=\dfrac{49}{2.9}+\dfrac{49}{9.16}+............+\dfrac{49}{65.72}\)

\(\Leftrightarrow F=\dfrac{7^2}{2.9}+\dfrac{7^2}{9.16}+............+\dfrac{7^2}{65.72}\)

\(\Leftrightarrow F=7\left(\dfrac{7}{2.9}+\dfrac{7}{9.16}+.............+\dfrac{7}{65.72}\right)\)

\(\Leftrightarrow F=7\left(\dfrac{1}{2}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...........+\dfrac{1}{65}-\dfrac{1}{75}\right)\)

\(\Leftrightarrow F=7\left(\dfrac{1}{2}-\dfrac{1}{72}\right)\)

\(\Leftrightarrow F=7.\dfrac{35}{72}=\dfrac{245}{72}\)

\(G=\dfrac{3}{1.3}+\dfrac{3}{3.5}+...........+\dfrac{3}{47.49}\)

\(\Leftrightarrow G=\dfrac{3.2}{1.3.2}+\dfrac{3.2}{3.5.2}+........+\dfrac{3.2}{47.49}\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+..........+\dfrac{2}{47.49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+........+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}\left(1-\dfrac{1}{49}\right)\)

\(\Leftrightarrow G=\dfrac{3}{2}.\dfrac{48}{49}=\dfrac{72}{49}\)

= 3/3 - 3/5 + 3/5 - 3/7 + ... + 3/47 - 3/49

= 3/3 - 3/49

= 46/49

= lưu ý : phép tính đầu là gach bỏ các số là : 3/5 + 3/5 - 5/7 + 5/7 - ... + 3/47

Chúc bạn học giỏi

Toán này lớp 6 bn ơi

A = 1.3 + 3.5 |+ 5.7 + ... + 97.99

6A = 1.3.6 + 3.5.(7-1) + 5.7.(9-3) + ... + 97.99.(101-95)

6A = 1.3.6 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ... + 97.99.101 - 95.97.99

6A = 1.3.6 + 97.99.101 - 1.3.5

6A = 3.(1 + 97.33.101)

2A = 1 + 323301 = 323302

A = 161651

~ Hok tốt ~

\(A=1.3+3.5+5.7+...+45.47+47.49\)

\(A=\left(1.49\right)+\left(2.3\right)+\left(2.5\right)+\left(2.7\right)+.....+\left(2.47\right)\)

\(A=49+2.\left(3+5+7+....+47\right)\)

Bây giờ ta phải tìm SSH của :

\(3+7+...+47\)

Vậy SSH của tổng đó là :

(47-3):2+1=23 (SSH)

=> \(A=49+2.\left(\frac{\left(47+3\right).23}{2}\right)\)

\(A=49+2.575\)

\(A=49+1150\)

\(A=1199\)

Dạng này lầm đầu gặp

\(6A=1.3.6+3.5.6+5.6.7+......+47.49.6=3+1.3.5+3.5.\left(7-1\right)+5.7.\left(9-3\right)+.....+47.49.\left(51-45\right)=3+1.3.5-1.3.5+3.5.7-......+47.49.51-45.47.49=47.49.51+3=3+141423=141426\Rightarrow A=23571\)

ngồi cả chục phút bấm máy tính ( Dùng hệ đếm cơ số N cho dễ nhin )

VÀ ĐÂY LÀ KẾT QUẢ ( ĐÃ KIỄM TRA KO SAI MỘT BIỂU THỨC , KO TIN AE CÓ THỂ DÙNG MÁY TÍNH KIỂM TRA )

\(=3.\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{47.49}\right)\)

\(=3.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

\(=3.\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

\(=3.\dfrac{46}{147}\)

\(=\dfrac{46}{49}\)

\(\dfrac{3}{3.5}+\dfrac{3}{5.7}+...+\dfrac{3}{47.49}\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

=\(\dfrac{3}{2}.\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

=\(\dfrac{3}{2}.\dfrac{46}{147}\)

=\(\dfrac{23}{49}\)

=3/2.(1/3-1/5+1/5-1/7+...+1/47-1/49)

=3/2.(1/3-1/49)

=3/2.46/147=23/49

Đặt A = \(\dfrac{3}{3.5}+\dfrac{3}{5.7}+\dfrac{3}{7.9}+...+\dfrac{3}{47.49}\)

2A = \(\dfrac{3.2}{3.5}+\dfrac{3.2}{5.7}+\dfrac{3.2}{7.9}+...+\dfrac{3.2}{47.49}\)

2A = 3\(\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{47.49}\right)\)

2A = 3 \(\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{47}-\dfrac{1}{49}\right)\)

2A = 3 \(\left(\dfrac{1}{3}-\dfrac{1}{49}\right)\)

2A = 3 . \(\dfrac{46}{147}\)

2A = \(\dfrac{46}{49}\)

=> A = \(\dfrac{46}{49}\) : 2

=> A = \(\dfrac{23}{49}\)

\(2H=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{49.51}\)

\(2H=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+...+\dfrac{51-49}{49.51}\)

\(2H=\dfrac{3}{1.3}-\dfrac{1}{1.3}+\dfrac{5}{3.5}-\dfrac{3}{3.5}+...+\dfrac{51}{49.51}-\dfrac{49}{49.51}\)

\(2H=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{49}-\dfrac{1}{51}\)

\(2H=1-\dfrac{1}{51}\)

\(2H=\dfrac{50}{51}\)

\(H=\dfrac{25}{51}\)