Toán Lớp 6: Tính nhanh : A=1.5+2.8+3.11+…+100.302
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Toán Lớp 6: Tính nhanh : A=1.5+2.8+3.11+…+100.302
Comments ( 1 )
=3.(1^2 + 2^2 + 3^2 + 4^2 + … + 100^2) + 2.(1 + 2 + 3 + 4 + 100)
=3. [1.(2-1) + 2.(3 – 1) + 3.(4 – 1) + 4.(5 – 1) + … + 100.(101 – 1)] + 2.100.(100 + 1): 2
=3.[(1.2 + 2.3 + 3.4 + 4.5 + … + 100.101) – (1 + 2 + 3 + 4 + … + 100)] + 100.101
=3.[(1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + … + 100.101.3) – 100.(100 + 1) : 2] + 100.101
=3.[(1.2.(3 – 0) + 2.3(4-1) + 3.4.(5 – 2) + … + 100. 101. (102 – 99) – 50.101] + 100.101
=3.[(1.2.3 – 0.1.2 + 2.3.4 – 1.2.3 + 3.4.5 – 2.3.4 + … + 100.101.102 – 99.100.101 – 50.101)] + 100.101
=3.[100.101.102 – 50.101] + 100.101
=101. 30550