Question

Tính nhanh:

\(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)

Answer 1

\(C=50^2-49^2+48^2-47^2+...+2^2-1^2\)

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

\(=99+95+...+3\)

\(=1275\)

Vậy C = 1275

Answer 2

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

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

\(C=50+49+48+....+2+1\)

\(C=\dfrac{\left(1+50\right).50}{2}=1275.\)

Answer 3

C = (50² - 49²) + (48² - 47²) + ... + (2² - 1²)

C = (50 - 49)(50 + 49) + (48 - 47)(48 + 47) + ... + (2 - 1)(2 + 1)

C = 99 + 97 + ... + 3 (bước này dễ, tự trình bày)

C = 2499

Answer 4

\(C=50^2-49^2+48^2-47^2+....+2^2-1^2\)

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

\(C=50+49+48+47+......+2+1\)

\(C=\left(50+1\right).25\)

\(\Rightarrow C=1275\)