đặt A=1^2+2^2+3^2+.....+50^2
=>A=1.1+2.2+3.3+.....+50.50
=>A=1(2-1)+2(3-1)+3(4-1)+.....+50(51-1)
=>A=1.2-1+2.3-2+3.4-3+.....+50.51-50
=>A=(1.2+2.3+3.4+....+50.51)-(1+2+3+...+50)
ĐẶT B=1.2+2.3+3.4+.....+50.51
C=1+2+3+.......+50
TA CÓ:A=B-C
B=1.2+2.3+3.4+.......+50.51
=>3B=1.2.3+2.3.3+3.4.3+....+50.51.3
=1.2.3+2.3.(4-1)+3.4(5-2)+.....+50.51(52-49)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+....+50.51.52-49.50.51
=50.51.52
=13260
=>B=44200
C=1+2+3+...+50
=(50+1).50:2
=1275
=>A=B-C=44200-1275=42925
12 + 22 + 32 + .... + 502
=1.1 + 2.2 + 3.3 + ... + 50.50
=1.( 2 - 1 ) + 2.( 3 - 1 ) + 3.( 4 - 1 ) + ... + 50( 51 - 1 )
= 1.2-1+2.3-2+3.4-3+....+50.51-50
=(1.2+2.3+3.4+...+50.51)-(1+2+3+3+...+50)
=\(\frac{50.51.52}{3}-\frac{50\left(50+1\right)}{2}\)
= ( tự tính )
