\(\frac{1.4}{4.6}+\frac{2.5}{6.8}+...+\frac{48.51}{98.100}\)

=> \(\frac{1}{4}.\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+...+\frac{48.52}{49.50}\right)\)

=> \(\frac{1}{4}.\left(\frac{2.3-2}{2.3}+\frac{3.4-2}{3.4}+...+\frac{49.50-2}{49.50}\right)\)

=> \(\frac{1}{4}.\left(1-\frac{2}{2.3}+1-\frac{2}{3.4}+...+1-\frac{2}{49.50}\right)\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2.3}-\frac{1}{3.4}-\frac{1}{49.50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\left(\frac{1}{2}-\frac{1}{50}\right)\right]\)

=> \(\frac{1}{4}.\left[48-2.\frac{12}{25}\right]\)

=> \(\frac{1}{4}.\frac{1176}{25}=\frac{249}{25}\)

\(Q=\frac{1}{4}\left(\frac{1.4}{2.3}+\frac{2.5}{3.4}+\frac{3.6}{4.5}+...+\frac{48.51}{49.50}\right)\)

\(=\frac{1}{4}\left(\frac{2.3-2}{2.3}+\frac{3.4-2}{3.4}+\frac{4.5-2}{4.5}+...+\frac{49.50-2}{49.50}\right)\)

\(=\frac{1}{4}\left(1-\frac{2}{2.3}+1-\frac{2}{3.4}+1-\frac{2}{4.5}+...+1-\frac{2}{49.50}\right)\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\right]\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\right)\right]\)

\(=\frac{1}{4}\left[48-2\left(\frac{1}{2}-\frac{1}{50}\right)\right]=\frac{294}{25}\)

\(A = 1.4 + 2.5 + 3.6 + ...+ 99.102\)

\(A=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2\)

\(A=(1.2+2.3+3.4+...+99.100)+2.(1+2+3+...+99)\)

\(A=333300+9900\)

\(A=343200\)

\(B = 2.4 + 4.6 + 6.8 + ....+ 98.100 + 100.102\)

\(B=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2) \)

\(B=4(1.2+2.3+...+50.51) \)

\(M= 1.2+2.3+...+50.51 \)

\(3M=1.2.3+2.3.(4-1)+...+50.51.(52-49) \)

\(=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51 \)

\(= 50.51.52\)

\(=132600 \)

\(\Rightarrow\)\(M=44200 \)

\(\Rightarrow\) \(B=4M=176800\)

trong sách nâng cao và phát triển 6 đó bạn

a,6B=2.4.6+4.6.(8-2)+...............+98.100.(102-96)

6B=2.4.6+4.6.8-2.4.6+..............+98.100.102-96.98.100

6B=98.100.102

B=98.100.102:6

B=166600

Đặt A = 8.10 + 10.12 + 12.14 + ....... + 98.100

=> 6A = 8.10.12 - 8.10.12 + 10.12.14 - 10.12.14 + ...... + 98.100.102

=> 6A =  98.100.102

=> A = 98.100.102/6

=> A = 166600

c.1.2.3+2.3.4+4.5.6+5.6.7=6+24+120+210

                                      =30+120+210

                                      =150+210

                                      =360

a) \(A=2.4+4.6+...+98.100\)

\(\Rightarrow6A=2.4.6+4.6.6+....+98.100.6\)

\(=2.4.6+4.6.\left(8-2\right)+...+98.100.\left(102-96\right)\)

\(=2.4.6+4.6.8-2.4.6+...+98.100.102-98.98.100\)

\(=98.100.102\)

\(=999600\)

\(\Rightarrow A=\frac{999600}{6}=166600\)

PHẦN khác tương tự mẹo là xem tích đầu tiên rồi nhân cả biểu thức đó với số liền sau của tích các số đầu nhưng mà có quy luật