已知1²+2²+3²+4²+……+n²=1/6n(n+1)(2n+1),求2²+4²+……+50²=
问题描述:
已知1²+2²+3²+4²+……+n²=1/6n(n+1)(2n+1),求2²+4²+……+50²=
答
2²+4²+……+50²
= 4(1²+2²+……+25²)
= 4 (1/6 * 25 * 26 * 51)
= 2*25*26*17
= 22100