Question

A= 1.2.3+2.3.4+3.4.5+..........+48.49.50

Answer 1

\(A=1.2.3+2.3.4+3.4.5+...+48.49.50\)

\(4A=1.2.3.4+2.3.4.4+3.4.5.4+...+48.49.50.4\)

\(4A=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+...+48.49.50.\left(51-47\right)\)

\(4A=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+...+48.49.50.51-48.48.49.50\)

\(4A=48.49.50.51\)

\(A=\dfrac{48.49.50.51}{4}=1499400\)

Answer 2

A=1499400 nhe ban !

Answer 3

4A=4.[1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 + . . . . . . + 48.49.50]
4A=1.2.3.4 +2.3.4.4 +3.4.5.4 +4.5.6.4 +.........+48.49.50.4
4A=1.2.3.4 +2.3.4.(5-1) + 3.4.5.(6-2) +4.5.6(7-3)+....+ 48.49.50(51-47)
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+....+ 48.49.50.51--47.48.49.50
4A =48.49.50.51
A=(48.49.50.51)/4

Answer 4

B = 1.2.3 + 2.3.4 +....+ 48.49.50
⇒⇒4B= 1.2.3.4 + 2.3.4.4 +.....+48.49.50.4
=1.2.3.4 + 2.3.4.(5-1) +.....+48.49.50.(51-47)
=1.2.3.4 + 2.3.4.5 - 1.2.3.4 +.....+ 48.49.50.51 - 47.48.49.50
=48.49.50.51= 1499400