证明[tex=15.429x1.357]19zJRHZLkC6S8SH5+5vjxNmRq8mCplTCVquB6R8BLZ7zkfP6/+etjCzUdXbWcPb9Ag9CTjVUL4C5MMQkkdlHoXb2F3VhmnzdCXuVeFYjAaY=[/tex]

证明不等式: [tex=15.429x1.357]TlD6jDemdN0jgQCR/2sOMLiqfRHQQeLXy1BgldLAnNxUTWVuR8IKWn1fBgSgkqhSH9mXb9ge4vsSQm/RnJuDaQ==[/tex]

证明 4 阶群  [tex=15.429x1.357]Amhl+PBo81QR/a5YBmmD1iW+rcbUQVZMF6Qf4JEHZH1S8Coc7v1gKGBIeIRn45h4[/tex]不同构于[tex=1.071x1.214]g5WMcNU3Hc8QxLvJ/c939w==[/tex]. 

证明: 4 阶群必同构于[tex=1.071x1.214]g5WMcNU3Hc8QxLvJ/c939w==[/tex]或[p=align:center][tex=15.429x1.357]ctVjCN8qwOmSe82Dsc3XUVVMWW+vz46RGF5CcwAG+APFQT6tqmLHF+FTakqpqgdm[/tex].

用 [tex=0.714x1.0]RRR4SYyCqv01G5bWEEMPdw==[/tex] 变换法解下列差分方程:[tex=15.429x1.357]gMwQaz2/ExLVCAocdRXTnoy25AnEBt0nQFns06d1ywvLDZQxc+G+HsD9dWBQcXOH[/tex][tex=12.929x1.357]pLSkoi1G+IEBLhqo3mZTeqKP7xU2fNTcxPVNglgc4cs=[/tex], 当 [tex=3.214x1.143]laUlyXtSABNgSGgFR/OHMg==[/tex] 时。

斐波那契数列时是[tex=10.5x1.214]q6g2kJf9hYxtDHBs0RpvP2X4Upk5H2JO44lZAioglX8=[/tex]，它满足[tex=15.429x1.357]Vn44GDY6dUKWZKmx5jsZKNW5ODbxpfZXUGod1WALfo4TmXjaQKxuKUjBxSw03Wr7M74uR4DPMzvjdZqBobWmFuqe0SjTXSr9qf7OmZUd0WdkDdtUDHpIkrfo4Y+A8B2WYdCG0n/kPZmE1h9cx4J+qRpCrYH3CMLXbZyTc9jFRQs=[/tex]求：斐波那契数列的通项公式.

求[tex=1.929x1.357]t0gYTFWPc2oOZUbnkzgAew==[/tex]，[tex=1.857x1.357]HPAY/8lZdPTeVaC829Iu0A==[/tex]使[tex=15.429x1.357]JNlAoK3ZaT13qtKkGDLOCh79MhHpxEc4+TV1E+mpOzpphEB/nV7g+unt2X9oQzFk[/tex]1)[tex=23.286x1.5]L59Y5+kRaQupUhESa/hPBldQ8/IwfD1NIpsnyOoeQRHWlmbKl1BoluycS3QCT2wl3042YJLCCeT8oldlUA5lkA==[/tex];2)[tex=24.0x1.5]fL7RyB9oDA3/XXX0mXPnkvQTxzYSXWM9cfMYA/PXMahfbisHrKMb04GstCEaEEJ+IWFIxN/GYn8oSBLNnxMraw==[/tex];3)[tex=19.357x1.5]Uicryhm26MjR2av6tKgP+OyFCxnyhsgADFw/eEPDUuXAIwRUqsb3ngptBheso/Wc[/tex].

设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex]，且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明，如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。

设[tex=15.429x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtkhSnIVg0YM+RT9EoYtnIRIBBCDLMZrxexPB7Q92nwqaNObvRfNr6fYoOxxOOB5KeWi8dul/72Aa7meWWDOofJ[/tex][tex=15.286x1.357]w1jiwhN28M7EUOfAKymDSvWjp6tLsrVLtIXWni4H/yqeUDeR7tgFdBDMMUqDi4C8Axoj5KcGYhKgXHI1eMxvFT2yqz8JU0J5G6ZVzZeoKkcA99jh3wF1mYUl6jKO+z7UhchjGZybAgTgnzm/cBb3yQ==[/tex]，且[tex=9.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTub7SnipdUJYMGMtGPDS5DqJ/Mr11NKCm+1NmpWlqOOpQ==[/tex]。证明，如果[tex=30.0x1.357]CKlOGn/4oc+CIjd/NrEXYPMrKY7YR6bQnYIT6RHXQTtZaVO0g6AJVDgZVz9tirIxrXANZ1N7F66XV5ymKSTY8VFNq8H9/9aRjFWO8CF4ueq3kBqAdofeE9+YnzZaPwQxFmJfebIORvJBMC47hDrAFP9fnVIxxOGh2MINi5k61+sLzQM7CsSPQ5syjoyb+o593oXxP00P0RPpEZNZeWR7wevjE8W+alPvRRHHNxhkXhA=[/tex]则[tex=15.357x1.357]vvUfMWB7qhXreignZ7ucHuuF3Eo9DkR508wp+cFQ3Ib//UZiNfe3Fdu2MSfHozk0YGaQO+5BMYnL+LBTAu3JTVzuInnPVyN/THdsdSGWGzc1odjTMsA5roIg5wjj/7oc[/tex]。

为了设计一个满足以下技术指标的模拟低通滤波器，比较用Butterworth滤波器,Chebyshev I型滤波器、Chebyshev II型滤波器和椭圆滤波器逼近时，所需的滤波器的[tex=0.857x1.0]HcQeTeQtUqN73yUJqDRZkQ==[/tex]。[tex=15.429x1.357]5tvL35050pMm36+UB1zZKBQRFTawyeNM9h/zL03nvBqdC6Xz0Qi031oVr5AUuDy+9ThbO3tOQ9PYfI+IY1fg8u4gq/ljAESBZ50mZ/kgBWNSfWqVkejMexRsAeAMZ/Uu[/tex]