a)

1 n   . 1 n + 1 = 1 n ( n + 1 ) 1 n   − 1 n + 1 = n + 1 − n n ( n + 1 ) = 1 n ( n + 1 ) ⇒ 1 n   . 1 n + 1 = 1 n   − 1 n + 1

b) Áp dụng kết quả trên để tính giá trị biểu thức sau:

M = 1 3.4 + 1 4.5 + 1 5.6 + 1 6.7 + 1 7.8 + 1 8.9 + 1 9.10 + 1 10.11 M = 1 3 − 1 4 + 1 4 − 1 5 + 1 5 − 1 6 + 1 6 − 1 7 + 1 7 − 1 8 + 1 8 − 1 9 + 1 9 − 1 10 + 1 10 − 1 11 M = 1 3 − 1 11 M = 8 33

\(B=19\cdot10-18\cdot9-17\cdot8-\cdots-12\cdot3-11\cdot2\)

\(=19\cdot10-2\left(2+9\right)-3\left(3+9\right)-\cdots-9\left(9+9\right)\)

\(=190-\left(2^2+3^2+\cdots+9^2\right)-9\left(2+3+\cdots+9\right)\)

\(=190+1-\left(1^2+2^2+\cdots+9^2\right)-9\cdot44\)

\(=191-\frac{9\left(9+1\right)\left(2\cdot9+1\right)}{6}-396=-205-\frac{9\cdot10\cdot19}{6}=-205-285=-490\)

Ta có:  B = 1 9.10 − 1 1.2 + 1 2.3 + ... + 1 7.8 + 1 8.9 = > B = − 79 90

Đáp án B

Đáp án là D

a ) 1 n ( n + 1 ) = n + 1 − n n ( n + 1 ) = n + 1 n ( n + 1 ) − n n ( n + 1 ) = 1 n − 1 n + 1

b ) 1 1.2 + 1 2.3 + ... 1 9.10 = 1 1 − 1 2 + 1 2 − 1 3 + ... + 1 9 − 1 10 = 9 10

a ) 1 n ( n + 1 ) = n + 1 − n n ( n + 1 ) = n + 1 n ( n + 1 ) − n n ( n + 1 ) = 1 n − 1 n + 1

b ) 1 1.2 + 1 2.3 + ... 1 9.10 = 1 1 − 1 2 + 1 2 − 1 3 + ... + 1 9 − 1 10 = 9 10

A = 1 - 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + . . . + 1 9 - 1 10 A = 1 - 1 10 = 9 10

Ta có:

1 1.2 + 1 3.4 + 1 5.6 + ... + 1 49.50

= 1 − 1 2 + 1 3 − 1 4 + 1 5 − 1 6 + ⋯ ⋯ + 1 49 − 1 50 = 1 + 1 3 + 1 5 + ⋯ ⋯ + 1 49 − 1 2 + 1 4 + 1 6 + ⋯ ⋯ + 1 50 = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ ⋯ + 1 50 − 2. 1 2 + 1 4 + 1 6 + ⋯ ⋯ + 1 50 = 1 + 1 2 + 1 3 + 1 4 + 1 5 + ⋯ ⋯ + 1 50 − 1 + 1 2 + 1 3 + ⋯ ⋯ + 1 25 = 1 26 + 1 27 + 1 28 + ... + 1 50       ( d p c m )