摘要:例3.当 成等差数列时.有a0-2a1+a2=0.当成等差数列时.有a0-3a1+3a2-a3=0.当a0.a1.a2.a3.a4成等差数列时.有a0-4a1+6a2-4a3+a4=0.由此归纳:当成等差数列时有,如果成等比数列.类比上述方法归纳出的等式为 .
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当a,a1,a2成等差数列时,有a+2a1-a2=0,当a,a1,a2,a3成等差数列时,有a-3a1+3a2-a3=0,当a,a1,a2,a3,a4成等差数列时,有a-4a1+6a2-4a3+a4=0,由此归纳:当a,a1,a2,…an成等差数列时有Cna-Cn1a1+Cn2a2-…+(-1)nCnnan=0,如果a,a1,a2,…an成等比数列,类比上述方法归纳出的等式为 .
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当a0,a1,a2成等差数列时,有a0+2a1-a2=0,当a0,a1,a2,a3成等差数列时,有a0-3a1+3a2-a3=0,当a0,a1,a2,a3,a4成等差数列时,有a0-4a1+6a2-4a3+a4=0,由此归纳:当a0,a1,a2,…an成等差数列时有Cn0a0-Cn1a1+Cn2a2-…+(-1)nCnnan=0,如果a0,a1,a2,…an成等比数列,类比上述方法归纳出的等式为 .
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