Gói kẹo thứ 2 nặng số kg là:

\(\dfrac{5}{4}-\dfrac{3}{4}=\dfrac{2}{4}=\dfrac{1}{2}\left(kg\right)\)

Đ/s:....

Vận tốc 2 xe là:

42+14 = 56 (km/h)

2h15p = 2,25 h

Độ dài quãng đường AB là:

2,25 x 56 = 126 (km)

Chiều cao hai đáy là:

\(15\times\dfrac{1}{3}=5\left(cm\right)\)

Diện tích hình thang là:

\(\dfrac{15\times5}{2}=37,5\left(cm^2\right)\)

\(a=15\times23,45+860\times2,345-2345\\ a=15\times2345\times\dfrac{1}{100}+860\times2345\times\dfrac{1}{1000}-2345\\ a=2345\times\left(15\times\dfrac{1}{100}+860\times\dfrac{1}{1000}-1\right)\\ a=2345\times0,01=23,45\)

Gọi số có 3 chữ số cần tìm là \(\overline{abc}\)

Ta biết: 

\(\overline{3abc}=\overline{abc}\times25\\ 3000+\overline{abc}=\overline{abc}\times25\\ \overline{abc}\times25-\overline{abc}=3000\\ \overline{abc}\times24=3000\\ \overline{abc}=125\)

Số số hạng từ 2;4;6.......;100 là: (100-2):2+1= 50 (số)

tổng : (2+100)x50:2 +105 =2655

a) Gọi \(2^0+2^1+...+2^{2017}\) là A

\(A=2^0+2^1+2^2+...+2^{2017}\\ 2A=2+2^2+2^3+....+2^{2018}\\ 2A-A=\left(2+2^2+2^3+....+2^{2018}\right)-\left(2^0+2^1+2^2+...+2^{2017}\right)\\ A=2^{2018}-1=4^x-1\\ =>2^{2018}=4^x=>4^{1009}=4^x=>x=1009\)

\(b,3^x+3^{x+1}+3^{x+2}+3^{x+3}=360\\ 3^x+3^x\cdot3+3^x\cdot3^2+3^x\cdot3^3=360\\ 3^x\left(1+3+3^2+3^3\right)=360\\ 3^x\cdot40=360\\ 3^x=9\\ 3^x=3^2\\ =>x=2\)

\(\left(\dfrac{1}{2}+1\right)\cdot\left(\dfrac{1}{3}+1\right)\cdot\left(\dfrac{1}{4}+1\right)\cdot...\cdot\left(\dfrac{1}{99}+1\right)\\ =\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot...\cdot\dfrac{100}{99}\\ =\dfrac{3\cdot4\cdot5\cdot...\cdot100}{2\cdot3\cdot4\cdot.....\cdot99}\\ =\dfrac{100}{2}=50\)

\(\dfrac{1}{2^2}< \dfrac{1}{1\cdot2};\dfrac{1}{3^2}< \dfrac{1}{2\cdot3};.....;\dfrac{1}{50^2}< \dfrac{1}{49\cdot50}\\ =>\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{50^2}< 1+\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+....+\dfrac{1}{49\cdot50}=1+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+....+\dfrac{1}{49}-\dfrac{1}{50}=\left(1+1\right)-\left(\dfrac{1}{2}-\dfrac{1}{2}\right)-\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-.....-\left(\dfrac{1}{49}-\dfrac{1}{49}\right)-\dfrac{1}{50}=2-0-0-0.....-\dfrac{1}{50}\\ =2-\dfrac{1}{50}< 2=>\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{50^2}< 2\)

\(\dfrac{13}{8}+\dfrac{9}{24}+\left(\dfrac{27}{8}+\dfrac{15}{24}\right)\\=\left(\dfrac{13}{8}+\dfrac{27}{8}\right)+\left(\dfrac{9}{24}+\dfrac{15}{24}\right)\\ =\dfrac{40}{8}+\dfrac{24}{24}\\ =5+1\\ =6\)