=> 9G=1.4.9+4.7.9+7.10.9+...+46.49.9

=2.4+1.4.7+4.7.10-1.4.7+7.10.13-4.7.10+10.13.16-7.10.13...46.49.52-43.46.49

=2.4+46.49.52

bn tự tính nhé

`#3107.101107`

1.

a)

`1/(1*4) + 1/(4*7) + 1/(7*10) + ... + 1/(100*103)`

`= 1/3 * (3/(1*4) + 3/(4*7) + 3/(7*10) + ... + 3/(100*103) )`

`= 1/3 * (1 - 1/4 + 1/4 - 1/7 + ... + 1/100 - 1/103)`

`= 1/3* (1 - 1/103)`

`= 1/3*102/103`

`= 34/103`

b)

`-1/3 + (-1/15) + (-1/35) + (-1/63) + ... + (-1/9999)`

`= - 1/3 - 1/15 - 1/35 - 1/63 - ... - 1/9999`

`= - (1/3 + 1/15 + 1/35 + ... + 1/9999)`

`= - (1/(1*3) + 1/(3*5) + 1/(5*7) + ... + 1/99*101)`

`= - 1/2 * (2/(1*3) + 2/(3*5) + 2/(5*7) + ... + 2/99*101)`

`= - 1/2* (1 - 1/3 + 1/3 - 1/5 + ... + 1/99 - 1/101)`

`= -1/2 * (1 - 1/101)`

`= -1/2*100/101`

`= -50/101`

2.

`3/(1*4) + 3/(4*7) + ... + 3/(94*97) + 3/(97*100)`

`= 1 - 1/4 + 1/4 - 1/7 + ... + 1/94 - 1/97 + 1/97 - 1/100`

`= 1-1/100`

`= 99/100`

\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)

\(A=2\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\right)\)

\(A=2\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)

\(A=2\left(1-\frac{1}{100}\right)\)

\(A=2.\frac{99}{100}=..............\)

Tự làm nốt nha

what?

\(A=1.4+4.7+7.10+....+97.100\)

\(2A=2.8+8.14+14.20+...+194.200\)

\(2A=2\left(1.4+4.7+7.10+...+97.100\right)\)

\(2A-A=2\left(1.4+4.7+...+97.100\right)-\left(1.4+4.7+...+97.100\right)\)

\(\Rightarrow A=2\)

Vậy.....

=2/3(3/1*4+3/4*7+...+3/97*100)

=2/3(1-1/4+1/4-1/7+...+1/97-1/100)

=2/3*99/100

=198/300

=66/100

=33/50