Question

[Phạm như quỳnh]

cho s= 2+2 mu 2+2 mu 3+ 2mu 4 +....+2 mu 99 +2 mu 100

a, tinh S

b,CHUNG MINH RANG S CHI HET CHO 3

Answer 1

[Đặng Hoàng Lâm]

a, S = 2 + 2² + 2³ + 2⁴ + ... + 2⁹⁹ + 2¹⁰⁰. 2S = 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰⁰ + 2¹⁰¹ => 2S - S = S = (2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰⁰ + 2¹⁰¹) - (2 + 2² + 2³ + 2⁴ + ... + 2⁹⁹ + 2¹⁰⁰) = 2¹⁰¹ - 2. Vậy S = 2¹⁰¹ - 2. b, S = 2 + 2² + 2³ + 2⁴ + ... + 2⁹⁹ + 2¹⁰⁰ = (2 + 2²) + (2³ + 2⁴) + ... + (2⁹⁹ + 2¹⁰⁰) = 2.(1 + 2) + 2³.(1 + 2) + ... + 2⁹⁹.(1 + 2) = (1 + 2).(2 + 2³ + ... + 2⁹⁹) = 3.(2 + 2³ + ... + 2⁹⁹) => S ⋮ 3. Vậy S ⋮ 3 (đpcm)