B=(99+1)x99/2

=4950

C=(999+1)x500/2

=250000

D=(998+10)x495/2

=249480

B = (99+1)x99:2=4950

C=(999+1)x500:2=250000

D = ( 998 + 10 ) x 495 : 2 = 249480

Ai thấy đúng ủng hộ nha !!!

S1= 1+2+3...+999

S1= (999-1) :1 +1= 999

S1= (999+1) x999 :2=499500 

S1= 499500

S2= ( 1010 -10) : 2 +1= 501

S2= (1010+ 10) x 501:2= 255510

Bài 1 :

\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(S=\frac{1}{1}-\frac{1}{2011}=\frac{2010}{2011}\)

Bài 2 :

\(S=\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}+...+\frac{1}{58}-\frac{1}{61}\)

\(S=\frac{1}{10}-\frac{1}{61}=\frac{51}{610}\)

Bài 3 :

\(3S=\frac{3}{4\times7}+\frac{3}{7\times11}+...+\frac{3}{19\times22}\)

\(3S=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{19}-\frac{1}{22}\)

\(3S=\frac{1}{4}-\frac{1}{22}\)

\(S=\frac{18}{88}\div3=\frac{6}{88}\)

Số số hạng là:(999-1):1+1=999(số)

Tổng dãy là:(999+1)x999:2=499500

Đ/S:499500

bang 499 500 .h  mik nha

a) quy luật là 1x1 = 1 ; 2x2 = 4 ; 3x3 = 9 ; 4x4 = 16 ...

b) số 625 là số hạng thứ 25

c) số hạng thứ 100 là số 10000

bài 2

tổng là 19110

có 10 chữ số sáu

mình ko chắc chắn đâu nha

có bài 1+4+9+16+......+100 bằng bao nhiêu

Bài 3: 

= 1- 1/2 + 1/2 -1/3 +...+ 1/98 -1/99

= 1- 1/99

= 98/99

Bài 4:

= 1/2*3 + 1/3*4 + 1/4*5 +...+  1/10*11

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +...+ 1/10 - 1/11

= 1/2 - 1/11= 9/22

a)\(\frac{4}{5}-\frac{1}{4}+\frac{3}{10}\)

\(=\frac{16}{20}-\frac{5}{20}+\frac{6}{20}\)

\(=\frac{17}{20}\)

b) \(\frac{2}{5}:\left(1-\frac{1}{10}\right)\)

\(=\frac{2}{5}:\frac{9}{10}\)

\(=\frac{4}{9}\)

c)\(\frac{7}{8}\times\frac{4}{9}+\frac{1}{14}:\frac{5}{14}\)

\(=\frac{7}{18}+\frac{1}{5}\)

\(=\frac{53}{90}\)

d)\(\frac{2}{7}\times\frac{3}{11}+\frac{2}{7}\times\frac{8}{11}\)

\(=\frac{2}{7}\times\left(\frac{3}{11}+\frac{8}{11}\right)\)

\(=\frac{2}{7}\times1=\frac{2}{7}\)

e) \(12+\left(16-11\right)\times4\)

\(=12+20=32\)

f)\(2\frac{3}{7}+1\frac{4}{7}\)

\(=\frac{17}{7}+\frac{11}{7}\)

\(=4\)

g)\(\frac{2}{3}\times\frac{4}{5}+\frac{1}{5}:\frac{9}{11}\)

\(=\frac{8}{15}+\frac{11}{45}\)

\(=\frac{7}{9}\)

h)\(\left(6,2:2+3,7\right):0,2\)

\(=\left(3,1+3,7\right):0,2\)

\(=6,8:0,2=34\)

#H

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)

\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)

\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+....+\frac{2}{x\left(x+1\right)}=\frac{499}{999}\)

\(\Leftrightarrow2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{499}{999}\)

\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{499}{999}\div2\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{499}{1998}\)

\(\Leftrightarrow\frac{1}{x+1}=\frac{250}{999}\)

\(\Leftrightarrow\left(x+1\right).250=999\Rightarrow x+1=\frac{999}{250}\Rightarrow x=\frac{999}{250}-1=\frac{749}{250}\)

Như kiểu đề sai hay sao ý