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1×2+2x3+3x4+4x5+n(n+1)
1x
2+2x3+3x4+4x5+
.
+n(n+1)
等于多少?急救! 请写下过程,谢谢
答:
1x
2+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)
1x
2+2x3+3x4+4x5+
.
+n(n+1)
等于多少?急救! 请写下过程,谢谢
答:
1x
2+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)
1x
2+2x3+3x4+4x5+
...
+n(n+1)
=?(n为正整数) 上面式子结果是多少?速...
答:
解
n(n+1)
=n²+n ∴原式 =
1+1
²+2+2²+
3+3
²+……
+n+n
²=(
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)...
1x
2+2x3+3x4+4x5+···n(n+1)
=___(n为自然数)
答:
n(n+1)=n^2+nS(n)=(1+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
)/6 =n(n+1)(n+2)/3
1x
2+2x3+3x4+4x5+
...
+n(n+1)
等于多少?急救!!
答:
公式三
1+2+3+
…+n=
n(n+1)
/2 上面的兄弟已经解答出来了。很正确,不过怕您不会用公式二。关于公式二的证明:1^2+2^2+3^2+……+n^2=n(n+1)(2n+1)/6 利用立方差公式 n^3-(n-1)^3=1*[n^2+(n-1)^
2+n(n
-1)]=n^2+(n-1)^2+n^2-n =2*n^2+(n-1)^2-n 2...
1X
2X3+2X3X4+3X4X5+
...
+N(N+1)
(N+2) 奥数题 要简便方法不要那个用微...
答:
回答:是不是这个公式 (n-1)
n(n+1)
=n^
3
-n {n^3}求和公式:Sn=[n(n+1)/
2
]^2 {n}求和公式:Sn=n(n+1)/2
简算1x
2+2x3+3x4+4x5+
...
+n(n+1)
答:
1x
2+2x3+3x4+4x5+
...
+n(n+1)
=(1^2+2^2+……n^
2)
+(1+2+3+……n)=n(n+1)(2n+1)/6+(1+n)xn/2 =n(n+1)(n+2)/3
1
x
2+2x3+3x4+4x5+
……+10x11 我要过程!!!
答:
1x
2+2x3+3x4+4x5+
……
+n(n+1)
=1²+2²+3²+...+n²+(1+2+3+...+n)=n(n+1)(2n+1)/6+n(n+1)/2 =n(n+1)(n+2)/3 1x2+2x3+3x4+4x5+……+10x11 =10×11×12/3 =440
1x
2+2x3+3x4+
...
+n(n+1)
=? 1x2x3+2x3x4+3x
4x5+
...+n(n+1)(n+2)=?
答:
(1*
1+1)
+(2*2+2)...=(1*1+2*2+3*3...
+N
*
N)
+(1+
2+3+4+
...+N)= 同理,第二题乘出来:(1*1*1+2*2*2+3*3*3+...n*n*
n)+3(1
*1+2*2...
+n
*n)+
2(1
+2+3+4+..+n)=
1
X
2+2X3+3X4+4X5
...+2011X2013=
答:
1X
2+2X3+3X4+4X5
...
+n(n+1)
=(1²+2²+3²+---+n²)+(1+2+3+---+n)=n(n+1)(2n+1)/6+n(n+1)/2 =(1/6)n(n+1)(2n+1+3)=n(n+1)(n+2)/3 把n=2012代入得:1X2+2X3+3X4+4X5...+2012X2013 =2012*2013*2014/3=2012*671*2014=27...
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涓嬩竴椤
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