Câu 1:
A) (32,5 + 28,3 x 2,7 - 108,91) x 2014
= (32,5 + 76,41 - 108,91) x 2014
= (108,91 - 108,91) x 2014
= 0.
B) 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90
= 1 - 1/2 + 1 - 1/6 + 1 - 1/12 + 1 - 1/20 + 1 - 1/30 + 1 - 1/42 + 1 - 1/56 + 1 - 1/72 + 1 - 1/90
= 9 - (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)
= 9 - [1/(1x2) + 1/(2x3) + 1/(3x4) + 1/(4x5) + 1/(5x6) + 1/(6x7) + 1/(7x8) + 1/(8x9) + 1/(9x10)]
= 9 - (1 - 1/2 + 1/2 - 1/3 + 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)
= 9 - (1 - 1/10)
= 9 - 9/10
= 81/10
Câu 2:
A) 22/7 - (11 - x) + 2/3 = 7/5
22/7 - (11 - x) = 7/5 - 2/3
22/7 - (11 - x) = 11/15
11 - x = 22/7 - 11/15
11 - x = 30/7
x = 11 - 30/7
x = 47/7
B) (x + 1) + (x + 2) + (x + 3) +....+ (x + 100) = 5550
100x + (1 + 2 + 3 + 4 +...+ 100) = 5550
100x + 5050 = 5550
100x = 500
Vậy suy ra:
x = 5.