1的平方加2的平方加3的平方直到n的平方 用C语言编程，1的平方加上2的平方加上3的平方一直加到n的平...
1\u5e73\u65b9\u52a02\u5e73\u65b9\u52a03\u5e73\u65b9\u4e00\u76f4\u52a0\u5230n\u5e73\u65b9\u7b49\u4e8e\u591a\u5c111²+2²+3²+\u2026\u2026+n²=n(n+1)(2n+1)/6\u3002\u53ef\u4ee5\u7528(n+1)³-n³=3n²+3n+1\u7d2f\u52a0\u5f97\u5230\u3002
\u8bc1\u660e\u8fc7\u7a0b\uff1a
\u6839\u636e\u7acb\u65b9\u5dee\u516c\u5f0f(a+1)³-a³=3a²+3a+1\uff0c\u5219\u6709\uff1a
a=1\u65f6\uff1a2³-1³=3\u00d71²+3\u00d71+1
a=2\u65f6\uff1a3³-2³=3\u00d72²+3\u00d72+1
a=3\u65f6\uff1a4³-3³=3\u00d73²+3\u00d73+1
a=4\u65f6\uff1a5³-4³=3\u00d74²+3\u00d74+1.\u00b7\u00b7
a=n\u65f6\uff1a\uff08n+1\uff09³-n³=3\u00d7n²+3\u00d7n+1
\u7b49\u5f0f\u4e24\u8fb9\u76f8\u52a0\uff1a
\uff08n+1)³-1=3\uff081²+2²+3²+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n²\uff09+3\uff081+2+3+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n\uff09+\uff081+1+1+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+1\uff09
3\uff081²+2²+3²+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n²\uff09=\uff08n+1\uff09³-1-3\uff081+2+3+.+n\uff09-\uff081+1+1+.+1\uff09
3\uff081²+2²+3²+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n²\uff09=\uff08n+1\uff09³-1-3\uff081+n\uff09\u00d7n\u00f72-n
6\uff081²+2²+3²+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n²\uff09=2\uff08n+1)³-3n\uff081+n)-2(n+1)=(n+1)[2(n+1)²-3n-2]
=(n+1)[2(n+1)-1][(n+1)-1]=n(n+1)(2n+1)
\u6240\u4ee51²+2²+\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7+n²=n\uff08n+1)\uff082n+1\uff09/6\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u7acb\u65b9\u5dee\u516c\u5f0f\u4e0e\u7acb\u65b9\u548c\u516c\u5f0f\u7edf\u79f0\u4e3a\u7acb\u65b9\u516c\u5f0f\uff0c\u4e24\u8005\u57fa\u672c\u63cf\u8ff0\u5982\u4e0b:
1\u3001\u7acb\u65b9\u548c\u516c\u5f0f\uff0c\u5373\u4e24\u6570\u7acb\u65b9\u548c\u7b49\u4e8e\u8fd9\u4e24\u6570\u7684\u548c\u4e0e\u8fd9\u4e24\u6570\u5e73\u65b9\u548c\u4e0e\u8fd9\u4e24\u6570\u79ef\u7684\u5dee\u7684\u79ef\u3002\u4e5f\u53ef\u4ee5\u8bf4\u4e24\u6570\u7acb\u65b9\u548c\u7b49\u4e8e\u8fd9\u4e24\u6570\u79ef\u4e0e\u8fd9\u4e24\u6570\u5dee\u7684\u4e0d\u5b8c\u5168\u5e73\u65b9\u7684\u79ef\u3002
2\u3001\u7acb\u65b9\u5dee\u516c\u5f0f\uff0c\u5373\u4e24\u6570\u7acb\u65b9\u5dee\u7b49\u4e8e\u8fd9\u4e24\u6570\u5dee\u4e0e\u8fd9\u4e24\u6570\u5e73\u65b9\u548c\u4e0e\u8fd9\u4e24\u6570\u79ef\u7684\u548c\u7684\u79ef\u3002\u4e5f\u53ef\u4ee5\u8bf4\uff0c\u4e24\u6570\u7acb\u65b9\u5dee\u7b49\u4e8e\u4e24\u6570\u5dee\u4e0e\u8fd9\u4e24\u6570\u548c\u7684\u4e0d\u5b8c\u5168\u5e73\u65b9\u7684\u79ef \u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1_\u7acb\u65b9\u5dee\u516c\u5f0f
int fun(int n)
{
int sum=0,i=0;
for(i=1;i<=n;i++)
{
sum+=i*i;
}
return sum;
}
∵（a+1）³-a³=3a²+3a+1（即（a+1)³=a³+3a²+3a+1）
a=1时：2³-1³=3×1²+3×1+1
a=2时：3³-2³=3×2²+3×2+1
a=3时：4³-3³=3×3²+3×3+1
a=4时：5³-4³=3×4²+3×4+1
。。。。。。
a=n时：（n+1）³-n³=3×n²+3×n+1
等式两边相加：
（n+1)³-1=3（1²+2²+3²+。。。+n²）+3（1+2+3+。。。+n）+（1+1+1+。。。+1）
3（1²+2²+3²+。。。+n²）=（n+1）³-1-3（1+2+3+。。。+n）-（1+1+1+。。。+1）
3（1²+2²+3²+。。。+n²）=（n+1）³-1-3（1+n）×n÷2-n
6（1²+2²+3²+。。。+n²）=2（n+1)³-3n（1+n)-2(n+1)
=(n+1)[2(n+1)²-3n-2]
=(n+1)[2(n+1)-1][(n+1)-1]
=n(n+1)(2n+1)
∴1²+2²+。。。+n²=n（n+1)（2n+1）/6.
求和吗？能用图吗
绛旓細1²+2²+3²=1+4+9 =14
绛旓細3脳(3+1)脳(3脳2+1)/6 =3脳4脳7/6 =14.
绛旓細14
绛旓細2^3-1^3=2*2^2+1^2-2 3^3-2^3=2*3^2+2^2-3 4^3-3^3=2*4^2+3^2-4 .n^3-(n-1)^3=2*n^2+(n-1)^2-n 鍚勭瓑寮忓叏鐩稿姞 n^3-1^3=2*(2^2+3^2+...+n^2)+[1^2+2^2+...+(n-1)^2]-(2+3+4+...+n)n^3-1=2*(1^2+2^2+3^2+...+n^2)...
绛旓細锛濓紙x锛1锛夛紙2x锛3锛夛紙x锛2锛/6 锛濓紙x锛1锛塠锛坸锛1锛夛紜1][2锛坸锛1锛+1]/6 涔熸弧瓒冲叕寮 4銆佺患涓婃墍杩,骞虫柟鍜屽叕寮1^2+2^2+3^2+鈥+n^2=n(n+1)(2n+1)/6鎴愮珛,寰楄瘉.璇佹硶浜岋紙鍒╃敤鎭掔瓑寮(n+1)^3=n^3+3n^2+3n+1锛夛細(n+1)^3-n^3=3n^2+3n+1,n^3-(n-1)^3=3...
绛旓細瑕佸垪鍑1鐨勫钩鏂瑰姞2鐨勫钩鏂瑰姞3鐨勫钩鏂涓鐩村姞鍒10鐨勫钩鏂圭殑椤癸紝鎴戜滑鍙互浣跨敤鏁板绗﹀彿鏉ヨ〃绀恒傝繖涓簭鍒楀彲浠ヨ〃绀轰负锛1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10²绠鍖栦竴涓嬶紝鎴戜滑鍙互鍐欐垚锛氣垜(n²), n浠1鍒10...
绛旓細瑙ｏ細鍏紡锛1²+2²+3²+...+n²=1/6 n(n+1)(2n+1)鎵浠 鍙杗=100锛屽緱 鍘熷紡=1/6 脳100脳锛100+1锛壝楋紙2脳100+1锛=338350
绛旓細+n2+(n+1)2+(n+2)2+(n+3)2+鈥+(n+n)2,姝ゆ璁鹃鏄В棰樼殑鍏抽敭,涓鑸汉涓嶄細杩欎箞鍘昏鎯.鏈変簡姝ゆ璁鹃,绗涓锛歋1=12+22+32+鈥+n2+(n+1)2+(n+2)2+(n+3)2+鈥+(n+n)2涓殑12+22+32+鈥+n2=S,(n+1)2+(n+2)2+(n+3)2+鈥+(n+n)2鍙互灞曞紑涓(n2+2n+12)+( n2+...
绛旓細涓鐨勫钩鏂瑰姞浜岀殑骞虫柟鍔犱笁鐨勫钩鏂路路路涓鐩村姞鍒皀鐨勫钩鏂 =n(n+1)(2n+1)/6
绛旓細鍏紡锛1²+2²+3²+.+N²=n锛坣+1锛(2n+1)/6 1鐨勫钩鏂瑰姞鍒100鐨勫钩鏂 =100脳101脳201锛6=338350
