1x1+2x2+3x3+4x4+5x5+6x6+7x7+8x8+9x9+10x10= 用简便方法来算 10x10一9x9 +8x8一7x7+6x6一5x5+4x4...

\\u7f16\u7a0b\u5e8f\u6c42Y=X1+2X2+3X3+4X4+5X5+6X6+7X7+8X8+9X9+10X10.

\u53c2\u8003\u7b54\u6848:\u8def\u6f2b\u6f2b\u5176\u4fee\u9053\u8fdc\uff0c\u543e\u5c06\u4e0a\u4e0b\u800c\u6c42\u7d22\u3002\u2014\u2014\u5c48\u539f

=\uff0810+9\uff09*\uff0810-9\uff09+\uff088+7\uff09*\uff088-7\uff09+\uff086+5\uff09*\uff086-5\uff09+\uff084+3\uff09*\uff084-3\uff09+\uff082+1\uff09*\uff082-1\uff09
=19+15+11+7+3
=48
\u671b\u91c7\u7eb3
\uff01\uff01\uff01

1(1X1)+49(7X7)+4(2X2)+36(6X6)+9(3X3)+81(9X9)+16(4X4)+64(8X8)+25(5X5)+100(10X10)=50+40+90+80+100+25=385

唉，我这个悲催的，我没读书了记不住公式了，这是求平方和的一道题，直接套用公式就行啦

浜旀牸涔樹互浜旀牸鏈夊灏戜釜姝ｆ柟褰?姹傝佸笀瑙ｇ瓟,鑳藉垪鍑鸿骞惰寰,璋㈣阿
绛旓細1X1鍗2X2鍗3X3鍗4X4鍗5X5 锛1鍗4鍗9鍗16鍗25 锛55涓 1X1琛ㄧず杈归暱涓5鐨1涓 2X2琛ㄧず杈归暱涓4鐨勬湁4涓 3X3琛ㄧず杈归暱涓3鐨勬湁9涓 4X4琛ㄧず杈归暱涓2鐨勬湁16涓 5X5琛ㄧず杈归暱涓1鐨勬湁25涓 鑷繁鍒嗗紑鏁版暟灏变細鏄庣櫧

绗竴涓浘1涓湀,绗簩涓浘4涓湀,绗洓涓浘16涓湀,闂涓変釜鍥惧嚑涓湀_鐧惧害...
绛旓細绗笁鍥惧簲璇ユ槸9涓 姣忎釜鍥惧湀鐨勪釜鏁板氨鏄繖涓綅缃暟瀛楀拰鑷繁鐨勪箻绉 绗1鍥撅細1x1=1 绗2鍥撅細2x2=4 绗3鍥撅細3x3=9 绗4鍥撅細4x4=16

1X1+2X2+3X3+4X4+5X5+鈥︹+NXN 姹傛鏁板垪鐨凷鍜
绛旓細s=x+2x^2+3x^3+4x^4+...+nx^n;xs=x^2+2x^2+3x^4+4x^5+...+nx^(n+1);(x-1)s=nx^(n+1)-(x+x^2+x^3+x^4+...+x^n)=nx^(n+1)-[x^(n+1)-x]/(x-1); s=[n/(x-1)]x^(n+1)-[x^(n+1)-x]/(x-1)^2 ...

1x1+2x2+3x3+4x4+...+nxn=1/6n(n+1)(2n+1) 26x26+27x27+28x28+29x29...
绛旓細瑙ｏ細1²+2²+3²+ 鈥+50²=1/6脳50脳(50+1)脳(2脳50+1)=42925 1²+2²+3²+ 鈥+25²=1/6脳25脳(25+1)脳(2脳25+1)=5525 涓婇潰涓ゅ紡鐩稿噺寰楋細26²+27²+鈥+50²=42925-5525=37400 绛旀锛37400 ...

1鍒10鐨勪簩娆℃柟,灏辨槸骞虫柟鏍广傛ユユユユユユユユユユユユユユユユユユ...
绛旓細1x1=1 2x2=4 3x3=9 4x4=16 5x5=25 6x6=36 7x7=49 8x8=64 9x9=81 10x10=100 sorry!閿欎簡锛屽簲璇ユ槸锛氣垰1=1 鈭2=1.414214 鈭3=1.73205 鈭4=2 鈭5=2.23607 鈭6=2.44949 鈭7=2.64575 鈭8=2.82843 鈭9=3 鈭10=3.16228 ...

鏁板浣撶Н闅鹃
绛旓細鎵浠=(2^6)x(3^3)/(2^5)/(3^2)=6锛屾墍浠ユ渶灏戣6鐩掓鏂逛綋绉湪锛屾墠鍙互鎺掓垚涓姝ｆ柟褰傚弬鑰: by myself 涓鐩掍互鍐呴兘鍙互鐮屽ソ澶氫釜姝ｆ柟褰 1x1 2x2 3x3 4x4 ... 16x16 璁 y 鏄洅鏁 绮掓暟渚挎槸 288y 绮 鑻ヨ鎺掓垚涓姝ｆ柟浣 绮掓暟渚挎槸 鏌 x 鐨3娆℃柟 鍗 x ^ 3 x^3 = 288y (y ...

1x1鍗2x2+3x3鍗4x4鍗5x5鍗佲100x100缁撴灉鐨勬湯浣嶆暟鏄嚑
绛旓細杩炵画骞虫柟鍜 Sn=n(n鍗1)(2n鍗1)/6 =100脳101脳201/6 =50脳67脳101 =5050脳67 鏈0鍑虹幇锛屾墍浠ユ湯浣嶏細0

|涓2x2鍗3x3涓4x4 5x5涓6x6鍗佲︹﹀崄99x99涓100x100鍗101x101=
绛旓細1x1锛2x2锛3x3锛4x4锛5x5锛6x6.锛100x100锛101x101 =1^2-2^2+3^2-4^2+5^2-6^2.-100^2+101^2 =(1-2)(1+2)+(3-4)(3+4)+.(99-100)(99+100)+101^2 =-(1+2+3+4.+99+100)+101^2 =-101*50+101^2 =101*(101-50)=5151 ...

1绛変簬1x1,1鍗3绛変簬2x2,1鍗3鍗5绛変簬3x3,1鍗3+5+7绛変簬4X4,浣犲彂鐜颁簡浠涔...
绛旓細鎴戝彂鐜颁簡姣忎釜绛変簬鍚庨潰閮芥湁涔樻硶鑰屼笖杩樻槸1x1锛岀劧鍚2x2锛屽張鐒跺悗3x3锛屾渶鍚庢槸4脳4銆

1x1-2x2+3x3-4x4鈥︹+99x99-100x100+101x101=
绛旓細1x1-2x2+3x3-4x4鈥︹+99x99-100x100+101x101 =1+(3²-2²)+(5²-4²)+...+(101²-100²)=1+3+2+5+4+銆傘傘+101+100 =1+2+3+...+101 =(1+101)脳101梅2 =51脳101 =5151

扩展阅读：1x2+2x3+3x4公式推导 ... 1x2十2x3十3x4裂项公式 ... modbus 1x 2x 3x 4x ... 1 2 3 4 5 6 ... 1x2+2x3+3x4+ 10x11 ... 摄像头1x模糊2x清楚 ... 1 2+2x3+3x4+4x5简算 ... 1 2 3 4 5 ... 巧算速算方法 1x2+2x3+3x4 ...