Question

tính tổng

1.2+2.3+3.4+...+99.100+100.101

Answer 1

đáp án:

bằng 343400

học tốt

Answer 2

Đặt A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100 + 100.101

3A = 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 + ... + 99.100.3 + 100.101.3

3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98) + 100.101.(102 - 99)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100 + 100.101.102 - 99.100.101

3A = 100.101.102

3A = 1030200

A = 343400

Answer 3

Đặt A=1.2+2.3+3.4+...+99.100+100.101

     3A=1.2.3+2.3.3+3.4.3+...+99.100.3+100.101.3

         =1.2.3+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)+100.101.(102-99)

         =1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100+100.101.102-99.100.101

        =100.101.102

\(\Rightarrow A=\frac{100.101.102}{3}\)

Answer 4

Đặt \(S=1.2+2.3+3.4+....+99.100+100.101\)

\(\Rightarrow3S=1.2.3+2.3.3+3.4.3+.....+99.100.3+100.101.3\)

\(\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+.....+99.100.\left(101-98\right)+100.101.\left(102-99\right)\)

\(\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.....+99.100.101-98.99.100+100.101.102-99.100.101\)\(\Rightarrow3S=100.101.102\)

\(\Rightarrow S=\frac{100.101.102}{3}\)

\(\Rightarrow S=\frac{1030200}{3}\)

\(\Rightarrow S=343400\)