Question

1.2.3.4+2.3.4.5+...+97.98.99.100

Answer 1

Đặt S=1.2.3.4+2.3.4.5+...+97.98.99.100

5S=1.2.3.4.5+2.3.4.5.5+...+97.98.99.100.5

5S=1.2.3.4.(5 - 0)+2.3.4.5.(6 - 1)+...+97.98.99.100.(101 - 96)

5S=1.2.3.4.5-0.1.2.3.4+2.3.4.5.6-1.2.3.4.5+...+97.98.99.100.101-96.97.98.99

5S=97.98.99.100.101

S=97.98.99.20.101

=>S=1901009880

Answer 2

Đặt A = 1.2.3.4 + 2.3.4.5 + ... + 97.98.99.100

5A = 1.2.3.4.5 + 2.3.4.5.5 + ... + 97.98.99.100.5

5A = 1.2.3.4.5 + 2.3.4.( 6 - 1 ) + ... + 97.98.99.100.( 101 - 96 )

5A = 1.2.3.4.5 + 2.3.4.5.6 - 1.2.3.4.5 + ... + 97.98.99.100.101 - 96.97.98.99.100

5A = 97.98.99.100.101

A = 97.98.99.100.101 : 5

A = 97.98.20.101

A = 19202120