Question

Calculati:
^2=la puterea a doua
2^2 +4^2+6^2+...90^2. Am nevoie de exercitiul asta repede, va rog!

Answer 1

e progresie aritmetica
si vei folosi formula: $1^{2}+2^{2}+...+n^{2}= \frac{n(n+1)(2n+1)}{6}$
$(1*2)^{2}$+$(2*2)^{2}$+$(2*3)^{2}$+...+$(2*45)^{2}$=
$1^{2}$·$2^{2}$+$2^{2}$·$2^{2}$+$2^{2}$·$3^{2}$+...+$2^{2}$·$45^{2}$=
$2^{2}$·($1^{2} + 2^{2} + 3^{2} +...+ 45^{2}$)=
$2^{2}$·$\frac{45(45+1)(2*45+1)}{6}$=
4·$\frac{45*46*91}{6}$=
$\frac{90*46*91}{3}$=125580