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A=1+3+32+...+3100
3A=3+32+33+...+3101
=>3A+1=1+3+32+...+3100+3101=A+3101
=>3A-A=3101-1
2A=3101-1
A=(3101-1)/2
B=1+4+42+...+450
4B=4+42+...+451
4B+1=1+4+42+...+450+451=B+451
=>4B-B=451-1
3B=451-1
B=(451-1)/3
A=1+3+32+...+3100
3A=3+32+33+...+3101
=>3A+1=1+3+32+...+3100+3101=A+3101
=>3A-A=3101-1
2A=3101-1
A=(3101-1)/2
B=1+4+42+...+450
4B=4+42+...+451
4B+1=1+4+42+...+450+451=B+451
=>4B-B=451-1
3B=451-1
B=(451-1)/3
2A = 3A - A = (3 + 32 + 33 + ... + 3101) - (1 + 3 + 32 + 33 + ... + 3100)
2A = 3101 - 1
A = \(\frac{3^{101}-1}{2}\)
3B = 4B - B = (4 + 42 + ... + 451) - (1 + 4 + 42 + ... + 450)
3B = 451 - 1
B = \(\frac{4^{51}-1}{3}\)
a)
Ta có :A=275=27.27.27.27.27 Ta có :B=2433=243.243.243
=(3.3.3).(3.3.3)...(3.3.3)(có 5 nhóm) =(3.3.3.3.3).(3.3.3.3.3)...(3.3.3.3.3)(có 3 nhóm)
=3.3.3.3.3...3(15 thừa số 3) =3.3.3.3.3...3.3(có 15 thừa số 3)
=315 =315
Mà315=315
Nên 275=2433
=>A=B
b)Ta có:A=85=8.8.8.8.8 B=27
=(2.2.2).(2.2.2)...(2.2.2)(có 5 nhóm)
=2.2.2.2.2.2..2(có 15 thừ số 2)
Mà 215>27
Nên 85>27
=>A>B
c)(bạn tự tìm người giải ,mình bó)
d)A=1+2+22+23+24+..+21999 B=22000
2.A=2.(1+2+22+23+...+21999)
2.A=2+22+23+24+...+21999+22000
Ta có:2.A-A=(2+22+23+24+...+22000) - (1+2+22+23+...+21999)
A=22000-1
Mà 22000-1<22000
Nên A<B
Câu2:
A=4+42+43+44+...+460
4.A=4.(4+42+43+...+460)
4.A=42+43+44+...+460+461
4.A-4=(42+43+44+...+461)-(4+42+43+...+460)
A=\(\frac{4^{61}-4}{3}\)
bài 3 thì mình quên cách làm rồi để mai mình xem vở chỉ cho
a) \(A=1+2+2^2+2^3+...+2^{60}\)
=>\(2A=2+2^2+2^3+2^4+...+2^{61}\)
=>\(2A-A=\left(2+2^2+2^3+2^4+...+2^{61}\right)-\left(1+2+2^2+2^3+...+2^{60}\right)\)
=>\(A=2^{61}-1\)
b) \(B=1+3+3^2+3^3+...+3^{46}\)
=>\(3B=3+3^2+3^3+3^4+...+3^{47}\)
=>\(3B-B=\left(3+3^2+3^3+3^4+...+3^{47}\right)-\left(1+3+3^2+3^3+...+3^{46}\right)\)
=>\(2A=3^{47}-1\)
=>\(B=\frac{3^{47}-1}{2}\)
c) \(C=1+5^2+5^4+...+5^{200}\)
=>\(5^2C=5^2+5^4+5^6+...+5^{202}\)
=>\(25C=5^2+5^4+5^6+...+5^{202}\)
=>\(25C-C=\left(5^2+5^4+5^6+...+5^{202}\right)-\left(1+5^2+5^4+...+5^{200}\right)\)
=>\(24C=5^{202}-1\)
=>\(C=\frac{5^{202}-1}{24}\)
a) A = \(1+2+2^2+2^3+...+2^{60}\)
2A = \(2.\left(1+2+2^2+2^3+...+2^{60}\right)\)
2A = \(2+2^2+2^3+2^4+...+2^{61}\)
2A - A = \(\left(2+2^2+2^3+2^4+...+2^{61}\right)\)- \(\left(1+2+2^2+2^3+...+2^{60}\right)\)
A = \(2^{61}-1\)
b)B = \(1+3+3^2+3^3+...+3^{46}\)
3B = \(3.\left(1+3+3^2+3^3+...+3^{46}\right)\)
3B = \(3+3^2+3^3+3^4+...+3^{47}\)
3B - B = \(\left(3+3^2+3^3+3^4+...+3^{47}\right)\)- \(\left(1+3+3^2+3^3+...+3^{46}\right)\)
2B = \(3^{47}-1\)
B = \(\left(3^{47}-1\right):2\)
a) 3.32.33.....3100=31+2+...+100
b)x.x3.x5.....x49=x1+3+5+...+49
2A = 3A - A = (3 + 32 + 33 + ... + 3101) - (1 + 3 + 32 + 33 + ... + 3100)
2A = 3101 - 1
A = \(\frac{3^{101}-1}{2}\)
3B = 4B - B = (4 + 42 + ... + 451) - (1 + 4 + 42 + ... + 450)
3B = 451 - 1
B = \(\frac{4^{51}-1}{3}\)