Question

giải chi tiết hộ mình bài này:

1.2.3 + 2.3.4 + 3.4.5 + ... + 99.100.101

mình đang cần gấp

Answer 1

Đặt \(C=1.2.3+2.3.4+3.4.5+...+99.100.101\)

\(4C=1.2.3.4+2.3.4.4+3.4.5.4+...+99.100.101.4\)

\(4C=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+....+99.100.101.\left(102-98\right)\)

\(4C=1.2.3.4+2.3.4.5+3.4.5.6+...+99.100.101.102\)

\(4C=99.100.101.102=101989800\)

\(\Rightarrow C=\frac{101989800}{4}=25497450\)

Answer 2

A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100).4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101

4A=98.99.100.101

A=98.99.100.101/4