Calculate : A = 1 x 2 x 3 + 2 x 3 x 4 +…+ 100 x 101 x 102

Calculate quickly : $\frac{8}{9}\times \frac{15}{16}\times \frac{24}{25}\times ...\times \frac{2499}{2500}$

( Write the result as a/b )

Calculate : 1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 +.............+ 99 x 100

A = 671 x 999…997 + 2013 ( factor 999…97 has 99 digits 9 totally )

Calculate the sum of all digits of A ?

Calculate :   A = 9 + 99 + 999 +....+  9.....9 (có 50 chữ số 9)

In the football tournament , there are k teams that played a match roundly ( two random teams play a match with each other ). The win team got 3 points. The peace team got 1 point and the lose team didn’t get point. Finishing the tournament, the win and lose match is 2 times the peace match. And the sum points of all team is 176. Find k ?

Given the sequence :$\frac{4}{3};\frac{9}{8};\frac{16}{15};\frac{25}{24};\frac{36}{35};...$ Find the product of 98 first terms of the sequence ?

( Write the result as a/b )   

 Calculate : A= $\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-...+\frac{197}{4851}-\frac{199}{4950}$

There is a natural number that has 2014 digits. Such that with 2 the consecutive digits in order of writing , to be a 2 – digit number that is divided by 17 or 23. If the last digit of that number is digit 1, find the first digit ?

Calculate : A=1 x 2 x 3 + 2 x 3 x 4 +…+ 100 x 101 x 102

Calculate the product of 98 fractions of the following sequence :

$\frac{4}{3}\times \frac{9}{8}\times \frac{16}{15}\times \frac{25}{24}\times ...\times \frac{9604}{9603}\times \frac{9801}{9800}$

( Write the result as a/b )

Calculate: A=  $\frac{2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2008}+\frac{1}{2009}}$  

A = $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{n}$ . Such that : A = $\frac{49}{50}$ . Find the value of n ?

A shop sold 75 bottle of oil, each bottle has $\frac{2}{5}$ liters oil. Such that the weight of each liter oil is $\frac{9}{10}$ kg. How many liters oil did the shop sell ?

A team has 60 friends, $\frac{3}{5}$ the number of friends is girls among them. How many girls are there ? How many boys are there ?