Ta có

P = x 10   –   13 x 9   +   13 x 8   –   13 x 7   +   …   -   13 x   +   10

=   x 10   –   12 x 9   –   x 9   +   12 x 8   +   x 8   –   12 x 7   –   x 7   +   12 x 6   +   …   + x 2   –   12 x   –   x   +   10     =   x 9 ( x   –   12 )   –   x 8 ( x   –   12 )   +   x 7 ( x   –   12 )   -   …   +   x ( x   –   12 )   –   x   +   10

Thay x = 12 vào P ta được

P   =   12 9 . ( 12   –   12 )   –   12 8 ( 12   –   12 )   +   12 7 ( 12   –   12 )             -   …   +   12 ( 12   –   12 )   –   12   +   10

= 0 + … + 0 – 2 = -2

Vậy P = -2

Đáp án cần chọn là: A

Ta có:

\(A=\frac{1}{2.3}+\frac{1}{6.5}+\frac{1}{10.7}+...+\frac{1}{198.101}\)

\(=\frac{2}{\left(2.3\right).2}+\frac{2}{\left(6.5\right).2}+\frac{2}{\left(10.7\right).2}+...+\frac{2}{\left(198.101\right).2}\)

\(=\frac{2}{2.\left(3.2\right)}+\frac{2}{6.\left(5.2\right)}+\frac{2}{10.\left(7.2\right)}+...+\frac{2}{198.\left(101.2\right)}\)

\(=\frac{2}{2.6}+\frac{2}{6.10}+\frac{2}{10.14}+...+\frac{2}{198.202}\)

\(=\frac{4}{2.6}:2+\frac{4}{6.10}:2+\frac{4}{10.14}:2+...+\frac{4}{198.202}:2\)

\(=\left(\frac{4}{2.6}+\frac{4}{6.10}+\frac{4}{10.14}+...+\frac{4}{198.202}\right):2\)

\(=\left(\frac{1}{2}-\frac{1}{202}\right):2\)

\(=\frac{50}{202}=\frac{25}{101}\)

Vậy \(A=\frac{25}{101}\)

frac,left,right là gì vậy ?

P = 18a + 30b + 7a - 5b = (18a + 7a) + (30b - 5b) = 25a + 25b = 25 . (a + b)

Thay a + b = 100 vào P = 25 . (a + b) ta được: P = 25 . 100 = 2500

(Dấu chấm là nhân nha bạn)

Cho M = ab + 18a ; biết a = 15; b = 18. Khi đó tính giá trị của A.

A = \(\frac{1}{1.2.4}+\frac{1}{2.4.5}+...+\frac{1}{8.10.11}+\frac{1}{10.11.13}\)

3 x A = \(\frac{3}{1.2.4}+\frac{3}{2.4.5}+...+\frac{3}{8.10.11}+\frac{3}{10.11.13}\)

3 x A = \(\frac{1}{1.2}-\frac{1}{2.4}+\frac{1}{2.4}-\frac{1}{4.5}+...+\frac{1}{8.10}-\frac{1}{10.11}+\frac{1}{10.11}-\frac{1}{11.13}\)

3 x A = \(\frac{1}{1.2}-\frac{1}{11.13}=\frac{1}{2}-\frac{1}{143}=\frac{143}{286}-\frac{2}{286}=\frac{141}{286}\)

A = \(\frac{141}{286}:3=\frac{141}{286.3}=\frac{47}{286}\)

C = x¹⁴ - 10x¹³ + 10x¹³ -10x¹¹ + ... + 10x¹² -10x + 10 

    = x¹⁴ - ( x + 1 )x¹³ + ( x + 1)x¹² -... - ( x + 1)x + 10 + 1

    =x¹⁴ -x¹⁴ - x¹³ + x¹³ + x¹² - ...- x² - x + 10 + 1 

     = 1

Không chắc lắm

Có x= 9 nên 10x^13=(9+1)x^13=(x+1)x^13=x^14+x^13
Tương tự thay vào C=x^14 - x^14 + x^13 - ....-x^2 - x +10=-x + 10=1

\(P=\dfrac{3\left(x^2+2x+3\right)+1}{x^2+2x+3}=3+\dfrac{1}{x^2+2x+3}=3+\dfrac{1}{\left(x+1\right)^2+2}\le3+\dfrac{1}{2}=\dfrac{7}{2}\)

\(P_{max}=\dfrac{7}{2}\) khi \(x=-1\)

\(M=\dfrac{2\left(x^2+3x+3\right)+1}{x^2+3x+3}=2+\dfrac{1}{x^2+3x+3}=2+\dfrac{1}{\left(x+\dfrac{3}{2}\right)^2+\dfrac{3}{4}}\le2+\dfrac{1}{\dfrac{3}{4}}=\dfrac{10}{3}\)

\(M_{max}=\dfrac{10}{3}\) khi \(x=-\dfrac{3}{2}\)