123,45 + 23,56 +76,44 + 54,55

= (123,45 + 54,55) + (23,56 + 76,44)

= 178 + 100

= 278

456 x 45 + 456 x 10 + - 456 x 55

=456 x (45 +10-55)

=456 x 0

=0

2,5 x 8,5 + 7,5 x 8,5 

=8,5 x (2,5 +7,5)

= 8,5 x 10

= 85

86 x 5 + 86 x 4 + 86

= 86 x (5+4+1)

= 86 x10

860

a)  Cách 1 :                                                          Cách 2

1 + 3 +5 + 7 + 9 + 11 + 13 + 15 + 17 + 19             1 + 3 +5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

=(1 + 19) + (3 + 17) +.... + (9 + 11)                   Áp dụng công thức tính dãy số ta có :

= 20 + 20 + ... + 20                                           \(\frac{\left[\left(19-1\right):2+1\right].\left(19+1\right)}{2}=\frac{10.20}{2}=10.10=100\)

= 20 x 5 = 100

b) giống bài a     nhưng cách 1 làm dài lắm , mình sẽ làm cách 2

áp dụng công thức tính dãy số ta có:

\(\frac{\left[\left(200-4\right):4+1\right].\left(200+4\right)}{2}=\frac{50.204}{2}=50.102=5100\)

[(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

help meeeeeeeeeeeeeee

mk chua gap dang nay bao gio

tớ  chưa học xin lỗi

1.3.77−1​+3.7.99−3​+7.9.1313−7​+9.13.1515−9​+\frac{19-13}{13.15.19}+13.15.1919−13​

=\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}=1.31​−3.71​+3.71​−7.91​+7.91​−9.131​+9.131​−13.151​+13.151​−15.191​

=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31​−15.191​=28595​−2851​=28594​

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)b,=61​.(1.3.76​+3.7.96​+7.9.136​+9.13.156​+13.15.196​)

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)c,=81​.(1.2.31​+2.3.41​+3.4.51​+...+48.49.501​)

=\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)=161​.(1.2.32​+2.3.42​+3.4.52​+...+48.49.502​)

=\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)=161​.(1.2.33−1​+2.3.44−2​+3.4.55−3​+...+48.49.5050−48​)

=\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)=161​.(1.21​−2.31​+2.31​−3.41​+3.41​−4.51​+...+48.491​−49.501​)

=\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}=161​.(21​−24501​)=161​.(24501225​−24501​)=4900153​

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)d,=75​.(1.5.87​+5.8.127​+8.12.157​+...+33.36.407​)

=\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)=75​.(1.5.88−1​+5.8.1212−5​+8.12.1515−8​+...+33.36.4040−33​)

=\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)=75​.(1.51​−5.81​+5.81​−8.121​+8.121​−12.151​+...+33.361​−36.401​)

=\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}=75​.(51​−14401​)=75​.(1440288​−14401​)=28841​

P/S: . là nhân nha

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

a) 1+2+3+...+2018

=[(2018-1):1+1].(2018+1):2

=2018.2019:2

=2037171

b) 4+7+10+13+...+2017

=[(2017-4):3+1].(2017+4):2

=672.2021:2

=679056

c) 1+2-3-4+5+6-7-8+9+10-11-12+13+14

=(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+13+14

=-4+(-4)+(-4)+13+14

=-12+27

=15

d) 23 x 75 + 25 x 23 + 180

=23 x (75+25) +180

=23 x 100 +180

=2300+180

2480

chúc ban hoc tốt nha

a) Số số hạng: ( 2018 - 1 ) : 1 + 1 = 2018

   Tổng:           2018 x ( 2018 + 1 ) : 2 = 2 037 171