C1:Số số hạng của dãy:

( 99 - 1 ) : 2 + 1 = 50 (số)

Tổng:

\(\frac{\left(99+1\right).50}{2}=2500\)

C2: 1+3+5+...+99

= (1+99)+(3+97)+(5+95)+...+(49+51) (có 25 cặp)

= 100+100+100+...+100 (25 số 100)

= 100 . 25 

= 2500

\(A=\dfrac{4}{1\cdot3}+\dfrac{4}{3\cdot5}+\dfrac{4}{5\cdot7}+...+\dfrac{4}{99\cdot101}\)

\(A=2\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{4}{99\cdot101}\right)\)

\(A=2\cdot\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(A=2\cdot\left(1-\dfrac{1}{101}\right)\)

\(A=2\cdot\dfrac{100}{101}\)

\(A=\dfrac{200}{101}\)

1/1*2+1/2*3+1/3*4+......+1/99*100+1/100*101

= 1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 100 + 1/00 - 1/101

= 1 - 1/101

= 100/101

3/5*8+3/8*11+3/11*14+.........3/605*608+3/608*611

= 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - ... + 1/608 - 1/611

= 1/5 - 1/611

= 606/3055

Ta có x = 99

=> x + 1 = 100

Khi đó A = x⁵ - 100x⁴ + 100x³ - 100x² + 100x - 9

= x⁵ - (x + 1)x⁴ + (x + 1)x³ - (x + 1)x² + (x + 1)x - 9

= x⁵ - x⁵ - x⁴ + x⁴ + x³ - x³ - x² + x² + x - 9

= x - 9 

Thay x = 99 vào A 

=> A = x - 9 = 99 - 9 = 90

Vậy A = 90

Ta có : \(x=99\Rightarrow100=x+1\)

\(A=x^5-100x^4+100x^3-100x^2+100x-9\)

\(=x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-9\)

\(=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-9\)

\(=x-9\)hay \(99-9=90\)

Vậy \(A=90\)

\(=\dfrac{3}{7}\cdot\left(\dfrac{4}{9}+\dfrac{5}{9}+1\right)=\dfrac{3}{7}\cdot2=\dfrac{6}{7}\)

\(=\dfrac{3}{7}\times\dfrac{4}{9}\times\dfrac{5}{9}\times\dfrac{3}{7}+\dfrac{3}{7}=\dfrac{3}{7}\times\left(\dfrac{4}{9}+\dfrac{5}{9}+1\right)=\dfrac{3}{7}\times2=\dfrac{6}{7}\)

=3/7 x (4/9 + 5/9) = 3/7 x1 =3/7

C =1+2-3-4+5+6-7-8+.....+97+98-99-100

= ( 1 + 2 -3 -4 ) + ( 5+6-7-8 ) + ... + ( 97 + 98 -99-100)

= 4 + ( -4 ) + ... + ( -4) ( do có 25 số)

= 4 x25 = 100

A= 1 + 2 - 3 -4 + 5 + 6 -7 -8 + ... +97 +98 -99 -100 ( có: ( 100 - 1 ) : 1 + 1 = 100 )

                   A= ( 1 +2 - 3 - 4 ) + ( 5 + 6 - 7 -8 ) + ... ( 97 + 98 - 99 +100 ) ( có 100 : 4 = 25 cặp )

                   A= - 4 + -4 + -4 + ... + -4 ( có 25 số hạng )

                   A= ( -4 ) . 25

                   A= -100

tham khảo