B=3/2-(3/2)^2+(3/2)^3-.........(3/2)^2014
= ( 3/2+ 3/2^ 3+ 3/2^ 5+...+3/2^ 2013)- ( 3/2^2+ 3/2^ 4+..+ ( 3/2)^ 2014)
=( 3/2+3/2^ 2+ 3/2^ 3+...+ 3/2 ^ 2014) -2.( 3/2^2+ 3/2^ 4+..+ ( 3/2)^ 2014)
Đặt A= 3/2+3/2^ 2+ 3/2^ 3+...+ 3/2 ^ 2014
⇒ 3/2. A= (3/2^ 2) + (3/2^3)+ ...+ ( 3/2) ^ 2015
3/2. A- A= ( (3/2^ 2) + (3/2^3)+ ...+ ( 3/2) ^ 2015) -(3/2+ (3/2^ 2) + (3/2^3)+ ...+ ( 3/2) ^ 2014)
1/2. A= ( 3/2) ^ 2015- 3/2
A= ( 3/2) ^ 2015- 3/2 ) . 2
Đặt C= 3/2^2+ 3/2^ 4+..+ ( 3/2)^ 2014
9/ 4. C= ( 3/2) ^ 4+ ( 3/2) ^6+..+( 3/2) ^ 2016
9/ 4. C- C= ( 3/ 2) ^ 2016- ( 3/2) ^ 2
C= (3/2) ^ 2016 -9/4) : 5/4
⇒ B= A - 2. C
= ( 3/2) ^ 2015- 3/2 ) . 2 - (3/2) ^ 2016 -9/4). 8/5
Đến đó bạn kiểm tra lại nha!Chúc học tốt!
