Toán Lớp 6: a, cho A =2 + 2 mũ 2 +2 mũ 3 + 2 mũ 4 + -. + 2 mũ 19 + 2 mũ 20 chứng tỏ A chia hết cho 3 b, Cho B = 1 + 3 + 3 mũ 2 + 3 mũ 3 + 3 mũ 4

Question

Toán Lớp 6:  a, cho A =2 + 2 mũ 2 +2 mũ 3 + 2 mũ 4 + ..... + 2 mũ 19 + 2 mũ 20 chứng tỏ A chia hết cho 3 b, Cho B = 1 + 3 + 3 mũ 2 + 3 mũ 3 + 3 mũ 4 +.... + 3 mũ 98 + 3 mũ 99 chứng tỏ B chia hết cho 4 c, cho C = 1 + 4 + 4 mũ 2 +4 mũ 3 + 4 mũ 4 + .... + 4 mũ 58 + 4 mũ 59 chứng tỏ C chia hết cho 5 , C chia hết cho 21

ngoclankhue · Answer

a, A = 2 + 2^2 + 2^3 + 2^4+...+ 2^20   = (2+2^2) + (2^3+2^4)+...+ (2^19 + 2^20)   = 2(1+2) + 2^3.(1+2) +...+ 2^19.(1+2)   = 2. 3 + 2^3. 3 +...+ 2^19. 3   = 3(2+...2^19) vdots 3   &rArr; A vdots 3(đpcm)   b, B = 1+3+3^2+3^3+...+3^98+3^99   = (1 + 3) + (3^2 + 3^3)+...+ (3^98 + 3^99)   = 1(1+3) + 3^2(1+3)+...+ 3^98.(1+3)   = 4 + 3^2. 4+...+ 3^98. 4   = 4(1+3^2+...+3^98) vdots 4   &rArr; B vdots 4 (đpcm)   c, C = 1 + 4 + 4^2 +...+ 4^59   = (1+4) + (4^2+4^3) +...+ (4^58 + 4^59)   = 1(1+4) + 4^2(1+4) +...+ 4^58(1+4)   = 1.5 + 4^2. 5+...+ 4^58. 5   = 5(1 +...+ 4^58) vdots 5   &rArr; C vdots 5 (đpcm)   C = 1 + 4 + 4^2 +...+ 4^59   = (1+4+4^2) +...+ (4^57 + 4^58 + 4^59)   = 1(1+4+4^2) +...+ 4^57(1+4+4^2)   = 1. 21 +...+ 4^57. 21   = 21(1+...+4^57) vdots 21   &rArr; C vdots 21 (đpcm)

maingoctruc · Answer

$  $   a,   A=2+2^2 + ... + 2^{19}+2^{20}   =>A=(2+2^2)+...+(2^{19}+2^{20})   =>A = 2 (1+2)+...+2^{19}(1+2)   => A = 2 . 3 + ... + 2^{19} . 3   =>A = 3 . (2+...+2^{19}) vdots 3   =>A vdots 3   b,   B=1+3 +...+3^{98}+3^{99}   =>B=(1+3)+...+(3^{98}+3^{99})   =>B = 4 . 1 + ... + 3^{98}  (1+3)   =>B=4.1 + ...+3^{98} . 4   =>B=4 . (1+...+3^{98}) vdots 4   =>B vdots 4   c,   Chứng minh C vdots 5   C=1+4+...+4^{58}+4^{59}   =>C=(1+4)+...+(4^{58}+4^{59})   =>C=5.1 + ... + 4^{58} (1+4)   =>C=5.1+...+4^{58} . 5   =>C=5.(1+...+4^{58}) vdots 5   =>C vdots 5   Chứng minh C vdots 21   C=1+4+4^2+...+4^{57}+4^{58}+4^{59}   =>C=(1+4+4^2)+...+(4^{57}+4^{58}+4^{59})   =>C=21 . 1 + ... + 4^{57} (1+4+4^2)   =>C = 21 . 1 + ... + 4^{57} . 21   =>C=21 . (1+...+4^{57}) vdots 21   =>C vdots 21