Question

S= 1²+2²+3²+.......+n²

Answer 1

S = 1 + (1+ 1).2 + (1 + 2).3 + (1+3).4 + ...+ (1 + n-1). n

S = 1 + (2+1.2) + (3+ 2.3) + (4 + 3.4) + ....+ ( n + (n -1).n)

S = (1+ 2  + 3 + 4 + ...+ n) + (1.2 + 2.3 + 3.4 + .....+ (n-1).n)

Tính B = 1+ 2+ 3 + ...+ n = (n +1).n/ 2

C = 1.2+ 2.3 + 3.4 + ...+ (n-1).n

=> 3.C = 1.2.3 + 2.3.3 + 3.4.3 + ...+ (n-1).n.3

3C = 1.2.3 + 2.3. (4 -1) + 3.4.(5 - 2) + ... + (n -1).n [(n+ 1) - (n -2)]

3C = [1.2.3 + 2.3.4 + ....+ (n-1).n.(n +1)] - (1.2.3 + 2.3.4 + ... + (n-2)(n -1).n)

3C = (n -1).n (n +1) => C = (n -1).n.(n +1)/ 3

VậyS = (n +1).n/ 2 + (n -1).n(n +1)/3

Answer 2

trả lời cho mik sớm nha trong vòng 10 h ai làm  dc mình thank you very much

Answer 3

+.......n²

Toán lớp 6

Huỳnh Thị Minh Huyền 15/08/2015 lúc 10:01

S = 1 + (1+ 1).2 + (1 + 2).3 + (1+3).4 + ...+ (1 + n-1). n

S = 1 + (2+1.2) + (3+ 2.3) + (4 + 3.4) + ....+ ( n + (n -1).n)

S = (1+ 2  + 3 + 4 + ...+ n) + (1.2 + 2.3 + 3.4 + .....+ (n-1).n)

Tính B = 1+ 2+ 3 + ...+ n = (n +1).n/ 2

C = 1.2+ 2.3 + 3.4 + ...+ (n-1).n

=> 3.C = 1.2.3 + 2.3.3 + 3.4.3 + ...+ (n-1).n.3

3C = 1.2.3 + 2.3. (4 -1) + 3.4.(5 - 2) + ... + (n -1).n [(n+ 1) - (n -2)]

3C = [1.2.3 + 2.3.4 + ....+ (n-1).n.(n +1)] - (1.2.3 + 2.3.4 + ... + (n-2)(n -1).n)

3C = (n -1).n (n +1) => C = (n -1).n.(n +1)/ 3

VậyS = (n +1).n/ 2 + (n -1).n(n +1)/3

Answer 4

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Answer 5

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Answer 6

có công thức a^m+b^m=(a+b)^m khong