解
展開する (42.6xπ+6.82.2ye)16
解
0.00101…x16π+0.00808…yex15π+0.03018…x14πy2e+0.07011…x13πy3e+0.11341…x12πy4e+0.13548…x11πy5e+0.12363…x10πy6e+0.08791…x9πy7e+0.04922…x8πy8e+0.02177…x7πy9e+0.00758…x6πy10e+0.00206…x5πy11e+0.00042…x4πy12e+0.00006…x3πy13e+6.97912E−6x2πy14e+4.63169E−7xπy15e+1.44086E−8y16e
解答ステップ
(42.6xπ+6.82.2ye)16
42.6xπ=0.65xπ
6.82.2ye=0.32352…ye
=(0.65xπ+0.32352…ye)16
2項定理を適用する: (a+b)n=i=0∑n(in)a(n−i)bia=0.65xπ,b=0.32352…ye
=i=0∑16(i16)(0.65xπ)(16−i)(0.32352…ye)i
総和を展開する
=0!(16−0)!16!(0.65xπ)16(0.32352…ye)0+1!(16−1)!16!(0.65xπ)15(0.32352…ye)1+2!(16−2)!16!(0.65xπ)14(0.32352…ye)2+3!(16−3)!16!(0.65xπ)13(0.32352…ye)3+4!(16−4)!16!(0.65xπ)12(0.32352…ye)4+5!(16−5)!16!(0.65xπ)11(0.32352…ye)5+6!(16−6)!16!(0.65xπ)10(0.32352…ye)6+7!(16−7)!16!(0.65xπ)9(0.32352…ye)7+8!(16−8)!16!(0.65xπ)8(0.32352…ye)8+9!(16−9)!16!(0.65xπ)7(0.32352…ye)9+10!(16−10)!16!(0.65xπ)6(0.32352…ye)10+11!(16−11)!16!(0.65xπ)5(0.32352…ye)11+12!(16−12)!16!(0.65xπ)4(0.32352…ye)12+13!(16−13)!16!(0.65xπ)3(0.32352…ye)13+14!(16−14)!16!(0.65xπ)2(0.32352…ye)14+15!(16−15)!16!(0.65xπ)1(0.32352…ye)15+16!(16−16)!16!(0.65xπ)0(0.32352…ye)16
簡素化 0!(16−0)!16!(0.65xπ)16(0.32352…ye)0:0.00101…x16π
簡素化 1!(16−1)!16!(0.65xπ)15(0.32352…ye)1:0.00808…yex15π
簡素化 2!(16−2)!16!(0.65xπ)14(0.32352…ye)2:0.03018…x14πy2e
簡素化 3!(16−3)!16!(0.65xπ)13(0.32352…ye)3:0.07011…x13πy3e
簡素化 4!(16−4)!16!(0.65xπ)12(0.32352…ye)4:0.11341…x12πy4e
簡素化 5!(16−5)!16!(0.65xπ)11(0.32352…ye)5:0.13548…x11πy5e
簡素化 6!(16−6)!16!(0.65xπ)10(0.32352…ye)6:0.12363…x10πy6e
簡素化 7!(16−7)!16!(0.65xπ)9(0.32352…ye)7:0.08791…x9πy7e
簡素化 8!(16−8)!16!(0.65xπ)8(0.32352…ye)8:0.04922…x8πy8e
簡素化 9!(16−9)!16!(0.65xπ)7(0.32352…ye)9:0.02177…x7πy9e
簡素化 10!(16−10)!16!(0.65xπ)6(0.32352…ye)10:0.00758…x6πy10e
簡素化 11!(16−11)!16!(0.65xπ)5(0.32352…ye)11:0.00206…x5πy11e
簡素化 12!(16−12)!16!(0.65xπ)4(0.32352…ye)12:0.00042…x4πy12e
簡素化 13!(16−13)!16!(0.65xπ)3(0.32352…ye)13:0.00006…x3πy13e
簡素化 14!(16−14)!16!(0.65xπ)2(0.32352…ye)14:6.97912E−6x2πy14e
簡素化 15!(16−15)!16!(0.65xπ)1(0.32352…ye)15:4.63169E−7xπy15e
簡素化 16!(16−16)!16!(0.65xπ)0(0.32352…ye)16:1.44086E−8y16e
=0.00101…x16π+0.00808…yex15π+0.03018…x14πy2e+0.07011…x13πy3e+0.11341…x12πy4e+0.13548…x11πy5e+0.12363…x10πy6e+0.08791…x9πy7e+0.04922…x8πy8e+0.02177…x7πy9e+0.00758…x6πy10e+0.00206…x5πy11e+0.00042…x4πy12e+0.00006…x3πy13e+6.97912E−6x2πy14e+4.63169E−7xπy15e+1.44086E−8y16e