[(1+100)*100]/2= 5050

SỐ ĐẦU + SỐ CUỐI NHÂN CHO SỐ SỐ HẠNG RỒI CHIA TẤT CẢ CHO 2

sai đề nhá, 9 chứ ko phải 999 đâu

\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)

\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)

\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)

\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)

làm giống như trên

\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)

\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)

\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)

\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)

\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)

\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)

\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)

\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)

\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)

P/S: . là nhân nha

sxasxsxxsxsxssxsxsxsxsx232332321322

1+2+3+4+5+6+7+8+9+..................+100=(1+99)+(2+98)+(3+97)+(4+96)+.......+100=100+100+100+.....+100=5000

chuc may man hihi

1+2+3+....+100

Từ 1 đến 100 có 100 số hạng

\(\Rightarrow1+2+3+...+100\)

\(=\frac{\left(100+1\right).100}{2}=5050\)

Tính nhanh:    35 \(\times\) 119 \(\times\) 0,25 \(\times\) 100 \(\times\) ( 3: 0,4 - 7,5)

                    =  35 \(\times\) 119 \(\times\) 0,25 \(\times\) 100 \(\times\) ( 7,5 - 7,5)

                    =  35 \(\times\) 119 \(\times\) 0,25 \(\times\) 100 \(\times\) 0

                   = 0

D=1/2²+1/3²+1/4²+1/5²+....+1/10²+1/11²

1/2²<1/1x2 ; 1/3²<1/2x3;...

=)D<1/1x2+1/2x3+1/3x4+1/4x5+...+1/9x10+1/10x11

D<1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11

D<1-1/11

D<10/11
 

Ta có: A = (1 - 2 ) + ( 3 -4 ) + ( 5 -6 ) + ...... + (99 - 100)

             = -1 + -1 + ........ + -1

            = -50

A=1-2+3-4+...+99-100( có 100 số,100 chia hết cho 2)

A=(1-2)+(3-4)+...+(99-100)( có 100:2=50 nhóm)

A=   -1  +  (-1) +...+  (-1)(50 số -1)

A= -1.50

A= -50

Câu B sai đề

bạn ghép 4 số đầu lại có kết quả là -8x325=-2600

\(1-2-3+4+5-6-7+8+...+97-98-99+100+101\)

\(=\left(1-2-3+4\right)+\left(5-6-7+8\right)+...+\left(97-98-99+100\right)+101\)

\(=0+0+...+0+101\)

\(=101\)

a, A=50(100+2):2-49(97+1):2=149

b, B=(1-3)+(2-4)+(5-7)+(6-8)+...+(297-299)+(298-300)+301+302

      =-2-2-2-...-2+301+302(150 chữ số 2)

      =-2.150+603

      =330