Câu hỏi của Trang Nguyễn

Question

Tính nhanh : 1 )S = ( 20²+18²+16²+...+2² ) - ( 19²+17²+...+1² )

2) Cho 1²+2

Nguyễn Việt Lâm · Accepted Answer

$S=20^2-19^2+18^2-17^2+...+2^2-1^2$

$S=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2-1\right)\left(2+1\right)$

$S=39+35+31+...+3$

$S=\frac{\left(3+39\right)}{2}.\left(\frac{39-3}{4}+1\right)=210$

2/ $1^2+2^2+3^2+...+10^2=385$

$\Rightarrow2^2\left(1^2+2^2+3^2+...+10^2\right)=2^2.385$

$\Rightarrow2^2+4^2+8^2+...+20^2=4.385=1540$

Câu trả lời:

$S=20^2-19^2+18^2-17^2+...+2^2-1^2$

$S=\left(20-19\right)\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2-1\right)\left(2+1\right)$

$S=39+35+31+...+3$

$S=\frac{\left(3+39\right)}{2}.\left(\frac{39-3}{4}+1\right)=210$

2/ $1^2+2^2+3^2+...+10^2=385$

$\Rightarrow2^2\left(1^2+2^2+3^2+...+10^2\right)=2^2.385$

$\Rightarrow2^2+4^2+8^2+...+20^2=4.385=1540$

Ngô Bá Hùng · Answer

1)$S=\left(20^2+18^2+16^2+...+2^2\right)-\left(19^2+17^2+...+1^2\right)\ S=20^2-19^2+18^2-17^2+...+2^2-1^2\ S=\left(20-19\right).\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2-1\right).\left(2+1\right)\ S=39+35+31+...+3\ S=\frac{\left(3+39\right)}{2}+\left(\frac{39-3}{4}+1\right)\ S=210$

2)$2^2+4^2+6^2+...+20^2\ =1^2.2^2+2^2.2^2+3^2.2^2+...+10^2.2^2\ =2^2.\left(1^2+2^2+3^2+...+10^2\right)\=4.385\ =1540 $

#tick&theo dõi

Câu trả lời:

1)$S=\left(20^2+18^2+16^2+...+2^2\right)-\left(19^2+17^2+...+1^2\right)\ S=20^2-19^2+18^2-17^2+...+2^2-1^2\ S=\left(20-19\right).\left(20+19\right)+\left(18-17\right)\left(18+17\right)+...+\left(2-1\right).\left(2+1\right)\ S=39+35+31+...+3\ S=\frac{\left(3+39\right)}{2}+\left(\frac{39-3}{4}+1\right)\ S=210$

2)$2^2+4^2+6^2+...+20^2\ =1^2.2^2+2^2.2^2+3^2.2^2+...+10^2.2^2\ =2^2.\left(1^2+2^2+3^2+...+10^2\right)\=4.385\ =1540 $

#tick&theo dõi

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