Question

Tính tổng A= 1.2 + 2.3 + 3.4 +. . . + 98. 99

Answer 1

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Answer 2

Ta có : A = 1.2 + 2.3 + 3.4 + ... + 98.99

=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ... + 98.99.3

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 98.99.(100 - 97)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +...+98.99.100 - 97.98.99 

=> 3A = 98.99.100

=> 3A = 970 200

=>   A = 323400

Answer 3

3A = 1 . 2 . 3 + 2 . 3 . 3  +  3 . 4 . 3 + . . . + 98 . 99 . 3 
= 1 . 2 . 3 + 2 . 3 (4  -  1) + 3 . 4 .( 5  -  2)  +. . . + 98 . 99 . ( 100 - 97) 
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + . . . + 98.99.100 - 97.98.99
= 1.2.3 -1.2.3 + 2.3.4 - 2.3.4 + 3.4.5- . . . - 97.98.99 + 98.99.100
= 98.99.100

\(\Leftrightarrow\)A = 98.99.100: 3 = 970200: 3 =323400