Question

tính nhanh \(1.2.3+2.3.4+3.4.5+...+98.99.100\)

Answer 1

đặt A=1.2.3+2.3.4+3.4.5+...+98.99.100

A.4=1.2.3.4+2.3.4.4+3.4.5.4+..+98.99.100.4

A.4=1.2.3(4-0)+2.3.4.(5-1)+3.4.5.(6-2)+......+98.99.100.(101-97)

a.4=1.2.3.4-0+2.3.4.5-2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100

A.4=98.99.100.101

A.4=97990200

A= 97990200:4

A=            24497550

Answer 2

Phải là phân số \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\) chứ !