Question:

IfΔr=∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣, then the value ofn𕒵∑r=1Δr:Depends only on aDepends only on nDepends both on a and nIs independent of both a and n.IfΔr=∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣, then the value ofn𕒵∑r=1Δr:Depends only on aDepends only on nDepends both on a and nIs independent of both a and n.Δr=∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣Δr=∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣Δr=∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣ΔrΔΔΔrrr==∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)r2r󔼕r𕒶n2n𕒵a12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)r2r󔼕r𕒶rrrr2r󔼔r�rr−�r𕒶3r𕒶33rr−𕒶2n2n𕒵an2n2n2n2nnn222n𕒵n𕒵nn−󔼓aaaa12n(n𕒵)(n𕒵)212(n𕒵)(3n𕒸)12n(n𕒵)12n(n𕒵)1212111222nn((nn−󔼓))(n𕒵)2(n𕒵)2((nn−󔼓)2)))22212(n𕒵)(3n𕒸)12(n𕒵)(3n𕒸)1212111222((nn−󔼓))((33nn−󔼴))∣∣∣∣∣∣∣∣∣∣∣∣∣∣∣n𕒵∑r=1Δrn𕒵∑r=1Δrn𕒵∑r=1Δrn𕒵∑r=1Δrn𕒵∑r=1Δrn𕒵∑r=1n𕒵∑r=1n𕒵∑n𕒵∑n𕒵∑n𕒵n𕒵n𕒵nn−󔼓∑∑∑r=1r=1r=1r=1rr==11ΔrΔΔΔrrrDepends only on aDepends only on nDepends both on a and nIs independent of both a and n.ADepends only on aDepends only on aBDepends only on nDepends only on nCIs independent of both a and n.Is independent of both a and n.DDepends both on a and nDepends both on a and n?