Question

[Nguyen Tung Lam]

Tính tổng:

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

Answer 1

[Dương Lam Hàng]

Ta có: \(S=1.2+2.3+3.4+...+99.100\)

\(\Rightarrow3S=1.2.3+2.3.3+3.3.4+....+99.100.3\)

\(\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)....99.100.\left(101-98\right)\)

\(\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(\Rightarrow3S=99.100.101\)

\(\Rightarrow S=\frac{99.100.101}{3}=\frac{999900}{3}=333300\)

Answer 2

[_ℛℴ✘_]

S=  1.2 + 2.3 +... + 99.100

=>S= \(\frac{99.100.101}{3}\)=333300