展开 (k(k-1)!(k+1)+(2k-1)!)/(k(2k-1)!(4k+1))

解答

展开

\frac{k ( k - 1 ) ! ( k + 1 ) + ( 2 k - 1 ) !}{k ( 2 k - 1 ) ! ( 4 k + 1 )}

\frac{k ^{2} ( k - 1 ) ! + k ( k - 1 ) ! + ( 2 k - 1 ) !}{4 k ^{2} ( 2 k - 1 ) ! + k ( 2 k - 1 ) !}

求解步骤

\frac{k ( k - 1 ) ! ( k + 1 ) + ( 2 k - 1 ) !}{k ( 2 k - 1 ) ! ( 4 k + 1 )}

乘开

k (2 k - 1)! (4 k + 1) : 4 k^{2} (2 k - 1)! + k (2 k - 1)!

= \frac{k ( k - 1 ) ! ( k + 1 ) + ( 2 k - 1 ) !}{4 k ^{2} ( 2 k - 1 ) ! + k ( 2 k - 1 ) !}

乘开

k (k - 1)! (k + 1) + (2 k - 1)! : k^{2} (k - 1)! + k (k - 1)! + (2 k - 1)!

= \frac{k ^{2} ( k - 1 ) ! + k ( k - 1 ) ! + ( 2 k - 1 ) !}{4 k ^{2} ( 2 k - 1 ) ! + k ( 2 k - 1 ) !}

e x p an d \frac{( 3 x ( x + 6 ) ^{3} )}{3} - (x + 6)^{3}

e x p an d \frac{( 2 x + 7 ) ( 1 - 5 x ) ( x + 2 )}{x ( 1 - x ) ^{2}}

e x p an d \frac{14 !}{( 14 - 4 ) 4 !}

e x p an d (x - 3)^{\frac{5}{3}} (x + 2)

e x p an d 15 (x + 3 = 60)