数列题,1的10次幂加2的10次幂,一直加到x的10次幂,有计祘公式吗
答案:2 悬赏:0
解决时间 2021-12-20 09:20
- 提问者网友：孤笛钟情你
- 2021-12-20 06:13
数列题,1的10次幂加2的10次幂,一直加到x的10次幂,有计祘公式吗
最佳答案
- 二级知识专家网友：风格单纯
- 2021-12-20 07:30
1^10+2^10+...+n^10=(6n^11+33n^10+55n^9-66n^7+66n^5-33n^3+5n)/66
附赠：
1：(n^2+n)/2
2：(2n^3+3n^2+n)/6
3：(n^4+2n^3+n^2)/4
4：(6n^5+15n^4+10n^3-n)/30
5：(2n^6+6n^5+5n^4-n^2)/12
6：(6n^7+21n^6+21n^5-7n^3+n)/42
7：(3n^8+12n^7+14n^6-7n^4+2n^2)/24
8：(10^9+45n^8+60n^7-42n^5+20n^3-3n)/90
9：(2n^10+10n^9+15n^8-14n^6+10n^4-3n^2)/20
10：(6n^11+33n^10+55n^9-66n^7+66n^5-33n^3+5n)/66
11：(2n^12+12n^11+22n^10-33n^8+44n^6-33n^4+10n^2)/24
12:(210n13+1365n12+2730n11-5005n9+8580n7-9009n5+4550n3-691n)/2730
13:(30n14+210n13+455n12-1001n10+2145n8-3003n6+2275n4-691n2)/420
14:(6n15+45n14+105n13-273n11+715n9-1287n7+1365n5-691n3+105n)/90
15:(3n16+24n15+60n14-182n12+572n10-1287n8+1820n6-1382n4+420n2)/48
16:(30n17+255n16+680n15-2380n13+8840n11-24310n9+44200n7-46988n5+23800n3-3617n)/510
17:(10n18+90n17+255n16-1020n14+4420n12-14586n10+33150n8-46988n6+35700n4-10851n2)/180
18:(210n19+1995n18+5985n17-27132n15+135660n13-529074n11+1469650n9-2678316n7+2848860n5-1443183n3+219335n)/3990
19:(42n20+420n19+1330n18-6783n16+38760n14-176358n12+587860n10-1339158n8+1899240n6-1443183n4+438670n2)/840
20:(330n21+3465n20+11550n19-65835n17+426360n15-2238390n13+8817900n11-24551230n9+44767800n7-47625039n5
+24126850n3-3666831n)/6930
21:(30n22+330n21+1155n20-7315n18+53295n16-319770n14+1469650n12-4910246n10+11191950n8-15875013n6+12063425n4
-3666831n2)/660
22:(30n23+345n22+1265n21-8855n19+72105n17-490314n15+2600150n13-10266878n11+28601650n9-52160757n7+55491755n5
-28112371n3+4272565n)/690
23:(30n24+360n23+1380n22-10626n20+96140n18-735471n16+4457400n14-20533756n12+68643960n10-156482271n8+221967020n6
-168674226n4+51270780n2)/720
附赠：
1：(n^2+n)/2
2：(2n^3+3n^2+n)/6
3：(n^4+2n^3+n^2)/4
4：(6n^5+15n^4+10n^3-n)/30
5：(2n^6+6n^5+5n^4-n^2)/12
6：(6n^7+21n^6+21n^5-7n^3+n)/42
7：(3n^8+12n^7+14n^6-7n^4+2n^2)/24
8：(10^9+45n^8+60n^7-42n^5+20n^3-3n)/90
9：(2n^10+10n^9+15n^8-14n^6+10n^4-3n^2)/20
10：(6n^11+33n^10+55n^9-66n^7+66n^5-33n^3+5n)/66
11：(2n^12+12n^11+22n^10-33n^8+44n^6-33n^4+10n^2)/24
12:(210n13+1365n12+2730n11-5005n9+8580n7-9009n5+4550n3-691n)/2730
13:(30n14+210n13+455n12-1001n10+2145n8-3003n6+2275n4-691n2)/420
14:(6n15+45n14+105n13-273n11+715n9-1287n7+1365n5-691n3+105n)/90
15:(3n16+24n15+60n14-182n12+572n10-1287n8+1820n6-1382n4+420n2)/48
16:(30n17+255n16+680n15-2380n13+8840n11-24310n9+44200n7-46988n5+23800n3-3617n)/510
17:(10n18+90n17+255n16-1020n14+4420n12-14586n10+33150n8-46988n6+35700n4-10851n2)/180
18:(210n19+1995n18+5985n17-27132n15+135660n13-529074n11+1469650n9-2678316n7+2848860n5-1443183n3+219335n)/3990
19:(42n20+420n19+1330n18-6783n16+38760n14-176358n12+587860n10-1339158n8+1899240n6-1443183n4+438670n2)/840
20:(330n21+3465n20+11550n19-65835n17+426360n15-2238390n13+8817900n11-24551230n9+44767800n7-47625039n5
+24126850n3-3666831n)/6930
21:(30n22+330n21+1155n20-7315n18+53295n16-319770n14+1469650n12-4910246n10+11191950n8-15875013n6+12063425n4
-3666831n2)/660
22:(30n23+345n22+1265n21-8855n19+72105n17-490314n15+2600150n13-10266878n11+28601650n9-52160757n7+55491755n5
-28112371n3+4272565n)/690
23:(30n24+360n23+1380n22-10626n20+96140n18-735471n16+4457400n14-20533756n12+68643960n10-156482271n8+221967020n6
-168674226n4+51270780n2)/720
全部回答
- 1楼网友：余生继续浪
- 2021-12-20 08:17
没有
我要举报
如以上问答内容为低俗、色情、不良、暴力、侵权、涉及违法等信息，可以点下面链接进行举报！
大家都在看
推荐资讯