Question

[Lê Ngọc Linh]

Bài 1: Tính nhanh

a, A = 1.4+ 2.5 + 3.6+ …+ 66.69

b, B = 1.50 + 2.49 + 3.48 + …+ 49. 2+ 50. 1

giúp mình nha, cảm ơn mọi người rất nhiều ạ. ai đúng mình se tich nhé

Answer 1

[Nguyễn Ngọc Anh Minh]

a/

\(A=1.2+1.2+2.3+2.2+3.4+3.2+...+66.67+66.2=\)

\(=\left(1.2+2.3+3.4+...+66.67\right)+2\left(1+2+3+...+66\right)\)

Đặt

\(B=1+2+3+...+66=\dfrac{66\left(1+66\right)}{2}=2211\)

Đặt 

\(C=1.2+2.3+3.4+...+66.67\)

\(3C=1.2.3+2.3.3+3.4.3+...+66.67.3=\)

\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+66.67.\left(68-65\right)=\)

\(=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-65.66.67+66.67.68=\)

\(=66.67.68\Rightarrow C=\dfrac{66.67.68}{3}=22.67.68\)

\(\Rightarrow A=C+2B\) Bạn tự tính nhé

b/

\(B=2\left(1.50+2.49+3.48+...+25.26\right)=\)

Ta có

\(C=1.50+2.49+3.48+...+25.26=\)

\(\left(50-49\right).50+\left(50-48\right).49+\left(50-47\right).48+...+\left(50-25\right).26=\)

\(=50.50-49.50+50.49-48.49+50.48-47.48+50.26-25.26=\)

\(=50.\left(26+27+28+...+50\right)-\left(25.26+26.27+27.28+...+49.50\right)\)

Ta có

\(D=26+27+28+...+50=\dfrac{25.\left(26+50\right)}{2}=950\)

Ta có

\(E=25.26+26.27+27.28+...+49.50\)

\(3E=25.26.3+26.27.3+27.28.3+...+49.50.3=\)

\(=25.26.\left(27-24\right)+26.27.\left(28-25\right)+...+49.50.\left(51-48\right)=\)

\(=-24.25.26+25.26.27-25.26.27+26.27.28-...-48.49.50+49.50.51=\)

\(=49.50.51-24.25.26\)

\(\Rightarrow E=\dfrac{49.50.51-24.25.26}{3}\)

\(\Rightarrow C=50D-E\)

\(B=2C\)

Bạn tự tính nhé