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とある無限積=無限和タイプの等式について
1.
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sha1_base64="gFWqo6Ju/D8ALl7PwnZasuC4swo=">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</latexit> n<latexit 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sha1_base64="gFWqo6Ju/D8ALl7PwnZasuC4swo=">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</latexit><latexit sha1_base64="gFWqo6Ju/D8ALl7PwnZasuC4swo=">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</latexit> 4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1<latexit sha1_base64="obVnReAV8QekWV0FcyDChsKafHk=">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</latexit><latexit 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sha1_base64="obVnReAV8QekWV0FcyDChsKafHk=">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</latexit><latexit sha1_base64="obVnReAV8QekWV0FcyDChsKafHk=">AAACe3ichVHLSsNAFD2Nr1ofrbpQcCPWilgpk1rxAYLoxmUf1goqJYnTGpomIUkLWvwBf8CFKxURUb/CjT/gop8gLiu4EfE2DYiKeoeZOXPmnjtnZmRTU22HsbpPaGvv6Ozydwd6evv6g6GBwU3bqFgKzyqGZlhbsmRzTdV51lEdjW+ZFpfKssZzcmmtuZ+rcstWDX3DOTD5blkq6mpBVSSHqHxoOLE8GxWX49E4dZGQGHVbPhRmMebG2E8geiAML5JG6Ao72IMBBRWUwaHDIaxBgk1tGyIYTOJ2USPOIqS6+xxHCJC2QlmcMiRiSzQWabXtsTqtmzVtV63QKRp1i5RjiLBHds0a7IHdsCf29mutmluj6eWAZrml5WY+eDySef1XVabZwf6n6k/PDgpYcL2q5N10meYtlJa+enjSyCylI7VJds6eyf8Zq7N7uoFefVEuUzx9igB9gPj9uX+CbDy2GBNTifDKqvcTfoxiHFP03PNYwTqSyLrHXuAWd753YUKYFmZaqYLP0wzhSwhzH06mjtY=</latexit> p(4) = 5<latexit sha1_base64="GFjBpJgv2P6mxj4mM1Bs744yGaU=">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</latexit><latexit sha1_base64="GFjBpJgv2P6mxj4mM1Bs744yGaU=">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</latexit><latexit sha1_base64="GFjBpJgv2P6mxj4mM1Bs744yGaU=">AAACaHichVHLSsNAFD2Nr1ofbXWh4qa0VHRTJlLxAULRjctWrRaqSBKnNTZNQpIWavEHXLkTdaUgIn6GG3/ART9BXCq4ceFNGhAt6h1m5syZe+6cmZFNTbUdxloBoau7p7cv2B8aGBwaDkeiI1u2UbMUnlcMzbAKsmRzTdV53lEdjRdMi0tVWePbcmXV3d+uc8tWDX3TaZh8tyqVdbWkKpJD1JY5nZ5ZntuLJFiKeRHrBKIPEvAja0RusYN9GFBQQxUcOhzCGiTY1IoQwWASt4smcRYh1dvnOEaItDXK4pQhEVuhsUyros/qtHZr2p5aoVM06hYpY0iyJ3bHXtkju2fP7OPXWk2vhuulQbPc1nJzL3wyvvH+r6pKs4ODL9Wfnh2UsOB5Vcm76THuLZS2vn509rqxtJ5sTrFr9kL+r1iLPdAN9PqbcpPj65cI0QeIP5+7E+RnU4spMZdOZFb8nwhiEnFM03PPI4M1ZJGnYw9xinNcBF6EqDAmTLRThYCvGcW3EOKfAk6K7Q==</latexit><latexit sha1_base64="GFjBpJgv2P6mxj4mM1Bs744yGaU=">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</latexit> 5 = 4 + 1 = 3 + 2 = 3 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1<latexit sha1_base64="P2g1MOhEr5d1/GzHviXdYyevJXU=">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</latexit><latexit 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sha1_base64="2vMwQPN5XGiEC+uUI1e9cpqUenQ=">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</latexit><latexit 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sha1_base64="2vMwQPN5XGiEC+uUI1e9cpqUenQ=">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</latexit><latexit 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4.
(n1, n2, ·
· · , nl)<latexit sha1_base64="ZrCi25hxGD13aIbFFG3Q1H77aCI=">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</latexit><latexit 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sha1_base64="pbmnwxiIDB9Cl/FSLY4Iq8VBtzA=">AAACY3ichVHLSsNAFD2Nr1ofrY+FIIJYFFflVgQfq6Ibl9YaW6hFkjjq0DQJSVrQ4g/oVnHhSkFE/Aw3/oCL/oAgLhXcuPA2DYiKeoeZOXPmnjtnZnTHlJ5P1Igobe0dnV3R7lhPb19/PDEwuOHZVdcQqmGbtlvQNU+Y0hKqL31TFBxXaBXdFHm9vNzcz9eE60nbWvf3HVGqaLuW3JGG5jOVlVuJJKUoiPGfIB2CJMJYtRPX2MQ2bBioogIBCz5jExo8bkWkQXCYK6HOnMtIBvsCh4ixtspZgjM0Zss87vKqGLIWr5s1vUBt8Ckmd5eV45ikB7qhF7qnW3qi919r1YMaTS/7POstrXC24kcjubd/VRWefex9qv707GMH84FXyd6dgGnewmjpawdnL7nFtcn6FF3SM/u/oAbd8Q2s2qtxlRVr54jxB6S/P/dPoM6kFlLp7GwysxT+RBSjmMA0P/ccMljBKlQ+VuAYJziNPCq9yqAy3EpVIqFmCF9CGfsASDWJvQ==</latexit> ni<latexit 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sha1_base64="HvID7UCoVoHFQRQh9tz5Qyr5mN0=">AAACZXichVHLSsNAFD2N7/pofSCCC8VScVVuRPCxKrpxqdZaQUtJ4liHpklI0oIWf0BwaxeuFETEz3DjD7jwDxSXCm5ceJsGRIt6h5k5c+aeO2dmdMeUnk/0GFHa2js6u7p7or19/QOx+ODQlmdXXENkDdu03W1d84QpLZH1pW+KbccVWlk3RU4vrTT2c1XhetK2Nv1DR+TLWtGS+9LQfKYyVkEW4glKURCTrUANQQJhrNnxa+xiDzYMVFCGgAWfsQkNHrcdqCA4zOVRY85lJIN9gWNEWVvhLMEZGrMlHou82glZi9eNml6gNvgUk7vLykkk6YFu6JXu6Zae6ePXWrWgRsPLIc96UyucQuxkLPP+r6rMs4+DL9Wfnn3sYyHwKtm7EzCNWxhNffWo/ppZ2kjWpumSXtj/BT3SHd/Aqr4ZV+ti4xxR/gD153O3guxsajGlrs8l0svhT3RjHFOY4eeeRxqrWEOWjy3iFGeoR56UAWVEGW2mKpFQM4xvoUx8Ai2Bip4=</latexit><latexit 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5.
1Y n=1 (1 xn ) 1 = X k=0 p(k)xk <latexit
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sha1_base64="ci8XKrdZo3Jt3jcVrFgcQcAIjeQ=">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</latexit> 1Y n=1 (1 xn ) 1 = (x0·1 + x1·1 + x2·1 + · · · ) <latexit sha1_base64="t5Nr+814X3xNCFfhBwQQkQrUwCo=">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</latexit><latexit sha1_base64="t5Nr+814X3xNCFfhBwQQkQrUwCo=">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</latexit><latexit sha1_base64="t5Nr+814X3xNCFfhBwQQkQrUwCo=">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</latexit><latexit sha1_base64="t5Nr+814X3xNCFfhBwQQkQrUwCo=">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</latexit> = 1X k=0 p(k)xk <latexit 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sha1_base64="L/matTI7Rdvfxjqy0H9GmpzhRdA=">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</latexit><latexit sha1_base64="L/matTI7Rdvfxjqy0H9GmpzhRdA=">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</latexit> · (x0·2 + x1·2 + x2·2 + · · · ) · (x0·3 + x1·3 + x2·3 + · · · ) = X k1,k2,··· 0 xk1·1+k2·2+··· <latexit sha1_base64="lzUcUoTlJfD8ydIKAg/WFZ/owzU=">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</latexit><latexit sha1_base64="lzUcUoTlJfD8ydIKAg/WFZ/owzU=">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</latexit><latexit sha1_base64="lzUcUoTlJfD8ydIKAg/WFZ/owzU=">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</latexit><latexit sha1_base64="lzUcUoTlJfD8ydIKAg/WFZ/owzU=">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</latexit>
6.
1Y n=1 (1 xn ) = 1X k=
1 ( 1)k x k(3k 1) 2 <latexit sha1_base64="Mh4p9q6xCTRpNhprgr9wjrxT8UY=">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</latexit><latexit 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sha1_base64="Mh4p9q6xCTRpNhprgr9wjrxT8UY=">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</latexit><latexit sha1_base64="Mh4p9q6xCTRpNhprgr9wjrxT8UY=">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</latexit> 1Y n=1 (1 xn ) = 1 + 1X i=1 (#Peven(i) #Podd(i))xi <latexit 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7.
1Y n=1 (1 xn )(1 zxn
1 )(1 xn /z) = 1X k= 1 ( 1)k zk x k(k 1) 2 <latexit sha1_base64="/LEs4R16VcMcn7VPoEanPxJxZZw=">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</latexit><latexit 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sha1_base64="FvwGwW9Q/LtmjwMygQNqQmpawhM=">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</latexit><latexit sha1_base64="FvwGwW9Q/LtmjwMygQNqQmpawhM=">AAACaXichVG7SgNBFD1Z3/EVtQnaBJeIVZgVwUcl2lj6WhOIQXbXUYfsi91JQIM/YGclmEpBRPwMG3/Awk8Q7RRsLLy7WRAV9Q4zc+bMPXfOzJi+LULJ2ENKaWvv6Ozq7kn39vUPDGaGhjdDrxZYXLc82wtKphFyW7hcl0LavOQH3HBMmxfN6lK0X6zzIBSeuyEPfF5xjD1X7ArLkEQVD3Nb0stp2xmVFVgcuZ9AS4CKJFa8zBW2sAMPFmpwwOFCErZhIKRWhgYGn7gKGsQFhES8z3GENGlrlMUpwyC2SuMercoJ69I6qhnGaotOsakHpMwhz+7ZNXthd+yGPbL3X2s14hqRlwOazZaW+9uDx9n1t39VDs0S+5+qPz1L7GI29irIux8z0S2slr5+ePqyPr+Wb0ywC/ZE/s/ZA7ulG7j1V+tyla81kaYP0L4/90+gTxXmCtrqtLqwmPxEN8Ywjkl67hksYBkr0GNzJzhDM/WsDCtZZbSVqqQSzQi+hKJ+ALBOi7o=</latexit> 1Y n=1 (1 xn )3 = 1X m=0 ( 1)m (2m + 1)x m(m+1) 2 <latexit 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8.
1Y n=1 (1 xn )d <latexit sha1_base64="f1RpFCIFfeVpbHtTxHVl/Be221s=">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</latexit><latexit
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