Question

Giúp mk nha mấy bạn,thứ 7 này mk nộp bài rồi

1.tính nhanh( ghi rõ từng cách tính,mà ko sử dụng máy tính)

a)1²-2²+3²-4²+....+2009²-2010²+2011²

b) 3(2²+1)(2⁴+1)(2⁸+1). ... .(2⁶⁴+1)+1

Giúp mk vs nha,

Answer 1

\(A=3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)....\left(2^{64}+1\right)+1\)

\(A=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)....\left(2^{64}+1\right)+1\)

\(A=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)......\left(2^{64}+1\right)+1\)

\(A=\left(2^8-1\right)\left(2^8+1\right)......\left(2^{64}+1\right)+1\)

\(A=\left(2^{64}-1\right)\left(2^{64}+1\right)+1\)

\(A=2^{128}-1+1=2^{128}\)

Answer 2

Câu 1:

\(A=1^2-2^2+3^2-4^2+....+2009^2-2010^2+2011^2\)

\(A=\left(1^2-2^2\right)+\left(3^2-4^2\right)+....+\left(2009^2-2010^2\right)+2011^2\)

\(A=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+....+\left(2009-2010\right)\left(2009+2010\right)+2011^2\)

\(A=\left(-1\right).3+\left(-1\right).7+....+\left(-1\right).4019+2011^2\)

\(A=\left(-3\right)+\left(-7\right)+.....+\left(-4019\right)+2011^2\)

\(A=\left(\dfrac{4019-3}{4}+1\right):2\left(-4019+-3\right)+2011^2=-2021005+404412=2023116\)