Giải thích các bước giải:
Ta có :
$S=2^2+3^2+..+49^2$
$\to S=2.2+3.3+..+49.49$
$\to S=2.(1+1)+3.(1+2)+..+49.(1+48)$
$\to S=(1.2+2.3+3.4+..+48.49)+(2+3+4+..+49)$
$\to S=\dfrac{1}{3}(1.2.3+2.3.3+3.4.3+..+48.49.3)+\dfrac{(49+2).48}{2}$
$\to S=\dfrac 13(1.2(3-0)+2.3(4-1)+3.4(5-2)+..+48.49(50-47))+1224$
$\to S=\dfrac 13(-0.1.2+1.2.3-1.2.3+2.3.4+..-47.48.49+48.49.50)+1224$
$\to S=\dfrac 13.48.49.50.+1224$
$\to S=40424$
