A = 2015 + 2015² + ... + 2015²⁰

2014.A = 2015.A - A = (2015² + 2015³ + ... + 2015²¹) - (2015 + 2015² + ... + 2015²⁰) = 2015²¹ - 2015 

=> A = \(\frac{2015^{21}-2015}{2014}\)

B = 3 + 3² + ... + 3⁹⁹

2.B = 3.B - B = (3² + 3³ + ... + 3¹⁰⁰) - (3 + 3² + ... + 3⁹⁹) = 3¹⁰⁰ - 3

=> B = \(\frac{3^{100}-3}{2}\)

1-2+3-4+...+2015

dãy trên có số các cặp số là:

\(\frac{\left(2014-1\right):1+1}{2}=1007\)

1-2+3-4+...+2015

= -1-1-1-...-1+2015

=-1x1007+2015

=-1007+2015

=1008

1-2+3-4+...+2015

=(1+3+5+...+2013+2015)-(2+4+6+...+2012+2014)

= A + B

Tính A = 1016064 và B = 1015056

A-B = 1008

Kết quả là 1008

 > \(\frac{1}{2}\)

a, \(5S=5^2+5^3+...+5^{2017}\)

\(5S-S=5^{2017}-5\)

\(S=\frac{5^{2017}-5}{4}\)

b,\(3S=3^2+3^3+...+3^{101}\)

\(3S-S=3^{101}-3\)

\(S=\frac{3^{101}-3}{2}\)

c, \(3S=3-3^2+3^3-...-3^{2016}\)

\(3S+S=1-3^{2016}\)

\(4S=1-3^{2016}\)

\(S=\frac{1-3^{2016}}{4}\)

b, 3S = 3^2+3^3+.....+3^101

2S=3S-S=(3^3+3^3+.....+3^101)-(3+3^2+....+3^100) = 3^101-3

=> S = (3^101-3)/2

Tk mk nha

A= 1 + ( -2 ) + 3 + ( -4 ) +...+ 2015 + ( -2016 ) 

A= [1 + ( -2 ) ]+ [3 + ( -4 )] +...+[ 2015 + ( -2016 ) ]

A= (-1)+(-1)+(-1)+(-1)+(-1)+..........+(-1)+(-1)=      (-1). [(2016-1):1+1]= (-1).2016=(-2016)

Hello bạn, mk cx tên Mai nek.

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

\(\Rightarrow\frac{2}{5}\left(x+1\right)=\frac{3}{5}-1\)

\(\Rightarrow\frac{2}{5}\left(x+1\right)=-\frac{2}{5}\)

\(\Rightarrow x+1=-\frac{2}{5}:\frac{2}{5}\)

\(\Rightarrow x+1=-1\)

\(\Rightarrow x=-1-1\)

\(\Rightarrow x=-2\)

\(\left(\frac{2}{7}\times x+1\right)\times\left(3-\frac{1}{2}\times x\right)=0\)

\(TH1:\frac{2}{7}\times x+1=0\)

\(\frac{2}{7}\times x=-1\)

\(x=-\frac{2}{7}\)

\(TH2:3-\frac{1}{2}\times x=0\)

\(\frac{1}{2}\times x=3\)

\(x=\frac{3}{2}\)

Vậy \(x\in\left\{\frac{3}{2};-\frac{2}{7}\right\}\)

1-1/2*2 * 1-1/3*3 *1-1/4*4-........1-1/2015*2015

=(1/2 *2/3*3/4..............2014/2015)*(.........)

Goi y cho roi do tu lam di

A = 1 + 1/2 + 1/3 + 1/4 + 1/5 + ... + 1/100

Ta đổi A = 2-1+1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100

A= 2 - 1 - 1/100 =200/100 -100/100 - 1/100

A= 99/100

Cảm ơn bạn Kudo Shinichi, nhưng 

1=2-1 ->ok

1/2=1-1/2 ->ok

1/3=1/2-1/3 -> sai 

vì 1/2-1/3=1/6