①当n=1时,左边=1,右边=1故此时原命题成立②当n≥2时,假设原命题仍成立令n=k得a1^2+a2^2+a3^2+``````+ak^2≥1/k 则当n=k+1时,a1^2+a2^2+a3^2+``````+ak^2+a^2(k+1)≥1/k+a^2(k+1)≥1/(k+1)故当n为任意正整数时,原命...