有理數(shù)計(jì)算奧數(shù)題

有理數(shù)計(jì)算奧數(shù)題有理數(shù)計(jì)算奧數(shù)題巧算458457原式=456x

456x457+456=456x457456x458=457333111112．．37x5681456．．456457456原式=（333+112111）xx568113711181137=（333x+x）1111121375681x=692+541=65413568135681+112x9x=合理分拆，化繁為簡計(jì)算：1-2+3-4+......+1997-1998+1999原式=1+(-2+3)+(-4+5)+......+(-1998+1999)=1+......+11000個1=1000(-51)2001x-52000(-x原式＝51－x51)2000(-5)200051(51＝－x2000)x(-5)2000＝－511x2x3+2x4x6+7x14x211x3x5+2x6x10+7x21x35原式＝1x2x3x(1+2x2x2+7x7x7)1x3x5x(1+2x2x2+7x7x7)＝5221+4181++161+321+641641-原式＝2141++81+161+321641+641+()641＝21+4181++161321+321+()-641＝21+4181++161161+()-＝......＝21+21()-641提取公因數(shù),整體約分

特點(diǎn):后一項(xiàng)是前一項(xiàng)的一半,

后一項(xiàng)加上它本身,就可得到前一項(xiàng)的值,增添輔數(shù),使問題解決.分?jǐn)?shù)計(jì)算5)+......+4521+(+3132)+(41+42+243)+(51+52+3++601(+602+603+......+6059)+......+原式=21+31+2+4+1+23++1+23

+45+......+1+2+3+45960=21+31x3+41x6+51x10+......+601x(1+59)x592=2(1+59)x59x2121+22+23+24+......+

259=1x21+2x31+3x41+......+1999x20001原式＝1-21+21-31+......+1999-2000111

＝1-2000＝200019995x91+9x131+13x171+......+101x1051原式＝41x(5-911+19-131+......+101-10511)＝211nx(n+1)1=n1-n+11nx(n+d)d=d1(n1-n+d1)1x2x31+2x3x41+......+98x99x1001原式＝12(1x21-2x31+2x31-3x41+......+98x991-99x1001)＝12(21-99x1001)＝198004949nx(n+1)x(n+2)1=12x(nx(n+1)1-(n+1)x(n+2)1)分?jǐn)?shù)數(shù)列的拆項(xiàng)S的末四位數(shù)字的和是多少？所以S的末四位數(shù)字的和為1＋9＋9＋5=24．2002132002加上它的12得到一個數(shù)，再加上所得的數(shù)的又得