Câu hỏi của nguyễn thị hồng gấm

Question

tính nhanh : 50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 - 1

@Nk>↑@ · Accepted Answer

$50^2-49^2+48^2-47^2+...+2^2-1$

$=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48-47\right)+...+\left(2-1\right)\left(2+1\right)$

$=99+95+...+3$

$=\frac{\left(99+3\right)\left[\left(99-3\right):4+1\right]}{2}$

$=\frac{102.\left(24+1\right)}{2}=\frac{102.25}{2}=1275$Câu trả lời: $50^2-49^2+48^2-47^2+...+2^2-1$

$=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48-47\right)+...+\left(2-1\right)\left(2+1\right)$

$=99+95+...+3$

$=\frac{\left(99+3\right)\left[\left(99-3\right):4+1\right]}{2}$

$=\frac{102.\left(24+1\right)}{2}=\frac{102.25}{2}=1275$

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