Tính nhanh tổng sau: A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90
Tính nhanh tổng sau: A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90
By Clara
By Clara
Tính nhanh tổng sau: A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90
Đáp án:
81/ 10
Giải thích các bước giải:
A = 1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90
A = 1 – 1/2 + 1 – 1/6 + 1 – 1/12 + 1 – 1/20 + ….. + 1/90
A = 9 – ( 1/2 + 1/6 + 1/12 + 1/20 + …….. + 1/90 )
A = 9 – ( 1/1.2 + 1/2.3 + 1/3.4 + 1/ 4.5 +…….+1/9.10 )
A = 9 – ( 1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 +……… + 1/9 – 1/10
A = 9 – ( 1 – 10 )
A = 9 – 9/10
A = 81/10
Đáp án: 81/10
Giải thích các bước giải:
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- (1/1×2+ 1/2×3 +1/3×4 +1/4×5 + 1/5×6 + 1/6×7 + 1/7×8 + 1/8×9 + 1/9×10 )
= 9- ( 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