1x2+2x3+3x4+99x100
徒苑欧1174求和:1X2+2X3+3X4+.+nX(n+1)? -
赫珠叙18030634994 ______[答案] 原式:f(x)=n(n+1)=1/3((n+2)(n+1)n-n(n-1)(n+1)) 运用数列的等差中的一些定理求出来,得1/3n(n+1)(n+2)
徒苑欧11741X2+2X3+3X4+.+99X100=?答案为333300 请问是怎么算的呀 -
赫珠叙18030634994 ______[答案] 第n项为 n(n +1)= n² + n 所以原式 = 1² + 2² + .+ 99² + 1 + 2 + .+ 99 = 99 * (99 + 1)*(2 * 99 + 1)/6 + (1 + 99)* 99 /2 就可以求出结果.
徒苑欧11741x2+2x3+3x4+4x5+...+n(n+1)=?(n为正整数)上面式子结果是多少?速求. -
赫珠叙18030634994 ______[答案] 解 n(n+1)=n²+n ∴原式 =1+1²+2+2²+3+3²+……+n+n² =(1+2+3+……+n)+(1²+2²+3²+……+n²) =(1+n)n÷2+1/6n(n+1)(2n+1) =n(n+1)[1/2+1/6(2n+1)] =n(n+1)(1/3n+2/3) =1/3n(n+1)(n+2) 公式 1²+2²+3²+……+n²=1/6n(n+1)(2n+1)
徒苑欧11741x2+2x3+3x4+4x5+.+n(n+1)+n(n+2)=? -
赫珠叙18030634994 ______[答案] 3n*(n+1) = n(n+1)(n+2) - (n-1)n(n+1) 所以3S = (n+1)(n+2)(n+3) - 0 S = (n+1)(n+2)(n+3) /3
徒苑欧11741x2+2x3+3x4+…+10x11=? -
赫珠叙18030634994 ______ 1x2+2x3+3x4+…+n(n+1)=1x(1+1)+2x(2+1)+3x(3+1)+…n(n+1)=(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n)=n(n+1)(2n+1)/6+n(n+1)/2=n(n+1)[(2n+1)+3]/61x2+2x3+3x4+…+10x11=10x(10+1)x[(10x2+1)+3]/6=110x4=440
徒苑欧11741x2+2x3+3x4+4x5+.+n(n+1)等于多少?急救!请写下过程,谢谢 -
赫珠叙18030634994 ______[答案] 1x2+2x3+3x4+…+n(n+1) =1^2+1+2^2+2+3^2+3+…+n^2+n =(1^2+2^2+3^2+…+n^2)+(1+2+3+…+n) =1/6*n(n+1)(2n+1)+1/2*n(n+1) =1/6*n(n+1)(2n+1+3)(提取公因式) =1/3*n(n+1)(n+2)
徒苑欧1174求使1x2+2x3+3x4+…+n(n+1) -
赫珠叙18030634994 ______[答案] 前面的变量声明自己解决,核心语句如下: (1)WHILE版 begin s:=0; n:=0; while s=2008; writeln('n=',n-1); end.
徒苑欧11741x2+2x3+3x4+...+n(n+1)=?1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)=? -
赫珠叙18030634994 ______[答案] n(n+1)(n+2)/3 n(n+1)(n+2)(n+3)/4 . 定义: n(n+1)(n+2)...(n+k)=[n]^k 则: ∑(i=1 to n)[n]^k=[n]^(k+1)/(k+1)=n(n+1)...(n+k+1)/(k+1)
徒苑欧11741x2+2x3+3x4.+99x100得数的简算方法 -
赫珠叙18030634994 ______[答案] 1x2+2x3+3x4.+99x100=2(1x2/2+2x3/2+3x4/2.+99x100/2)=2[C(2,2)+C(3,2)+C(4,2)+.+C(100,2)]=2[C(3,3)+C(3,2)+C(4,2)+.+C(100,2)]连续利用公式C(n,m)+C(n,m-1)=C(n+1,m)=2*C(100,3)=2*100*99*98/6=323400
徒苑欧11741x2+2x3+3x4+4x5······100x101答案是几? -
赫珠叙18030634994 ______[答案] 1*2+2*3+3*4+.+100*101 =1/3*1*2*3+1/3[2*3*4-1*2*3]+1/3[3*4*5-2*3*4]+.+1/3[100*101*102-99*100*101] =1/3[1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+...+100*101*102-99*100*101] =1/3*100*101*102 =343400