1. The document is an English language learning exercise that presents sentences in Mongolian with blanks to be filled in with English verbs. It covers topics like present continuous tenses, verb phrases, and filling in missing verbs.
2. The exercises include choosing the correct verbs to fill in blanks and match verb phrases with situations. Examples ask about what noises people are hearing, what friends are doing on holiday, and whether people enjoy their jobs or classes.
3. The purpose is to practice English verb tenses and verb phrases in sentences about common situations to build English language skills.
1. The document is an English language learning exercise that presents sentences in Mongolian with blanks to be filled in with English verbs. It covers topics like present continuous tenses, verb phrases, and filling in missing verbs.
2. The exercises include choosing the correct verbs to fill in blanks and match verb phrases with situations. Examples ask about what noises people are hearing, what friends are doing on holiday, and whether people enjoy their jobs or classes.
3. The purpose is to practice English verb tenses and verb phrases in sentences about common situations to build English language skills.
Презентація знайомить учнів з розміщеннями без повторень, формулою для числа розміщень з n елементів по m елементів та прикладами розв'язувати нескладні комбінаторні задачі.
The document contains three mathematical proofs:
1. Using induction, it is proven that for any natural number n, the sum 2 + 4 + 6 + ... + 2n is equal to n(n+1).
2. Also by induction, it is shown that the sum 1/(3*5) + 1/(5*7) + ... + 1/(2n+1)(2n+3) equals n/(3(2n+3)) for any natural n.
3. Finally, induction is used to prove that for any natural number n, the expression 8n + 6 is divisible by 7.
Презентація знайомить учнів з розміщеннями без повторень, формулою для числа розміщень з n елементів по m елементів та прикладами розв'язувати нескладні комбінаторні задачі.
The document contains three mathematical proofs:
1. Using induction, it is proven that for any natural number n, the sum 2 + 4 + 6 + ... + 2n is equal to n(n+1).
2. Also by induction, it is shown that the sum 1/(3*5) + 1/(5*7) + ... + 1/(2n+1)(2n+3) equals n/(3(2n+3)) for any natural n.
3. Finally, induction is used to prove that for any natural number n, the expression 8n + 6 is divisible by 7.