2.A= \(2+2^2+2^3+2^4+........+2^{64}\)
2.A-A= \(2+2^2+2^3+2^4+.........+2^{64}-1-2-2^2-2^3-....-2^{63}\)
A= \(2^{64}-1\)
k mk nha
B1:
2A=2+22+23+24+...+264
2A - A=(2+22+23+24+...+264) - (1+2+22+23+...+263)
A=264 - 1
5B=52+53+54+...+5101
5B - B=(52+53+54+...+5101) - (5+52+53+...+5100)
4B=5101- 5
B = \(\frac{5^{101}-5}{4}\)
4C=4+42+43+44+...+42017
4C - C=(4+42+43+44+...+42017) - (1+4+42+43+...+42016)
3C=42017-1
C=\(\frac{4^{2017}-1}{3}\)
B2:
ta có:
A=1+2+22+...+22002
2A=2+22+23+...+22003
2A - A=(2+22+23+...+22003)-(1+2+22+...+22002)
A=22003 - 1
vì 22003 - 1<22003 mà A=22003 - 1; B=22003
Vậy A<B
A = 5 + 52 + 53 + . . . + 5100
5A = 5. ( 5 + 52 + 53 + . . . + 5100)
5A = 52 + 53 + 54 + . . .+ 5 101
5A - A = ( 52 + 53 + 54 + . . . + 5101 ) - ( 5 + 52 + 53 + . . . + 5100 )
4A = 5101 - 5
A = 5101 - 5 : 4
