Question

tinh s

S=1.2+2.3+3.4+4.5+5.6+....+99.100

Answer 1

S = 1.2 + 2.3 + ... + 99.100

4S = 1.2.(3 - 0) + 2.3.(4 - 1) + ... + 99.100.(101 - 98)

4S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 99.100.101 - 98.99.100

4S = (1.2.3 + 2.3.4 +...+ 99.100.101) - (0.1.2 + 1.2.3 +...+ 98.99.100)

4S = 99.100.101 - 0.1.2

4S = 99.100.101

S = 99.25.101

S = 249975

Answer 2

\(S=1.2+2.3+3.4+4.5+5.6+...+99.100\)

\(3S=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3\)

\(3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+4.5.\left(6-3\right)+...+99.100.\left(101-98\right)\)\(1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101+98.99.100\)

\(3S=\left(1.2.3-1.2.3\right)+\left(2.3.4-2.3.4\right)+...+\left(98.99.100-98.99.100\right)+99.100.101\)

\(3S=99.100.101=9999000\)

\(S=9999000:3=3333000\)

\(\Rightarrow S=3333000\)