Rút gọn : a) M = \(2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
b) N = \(3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)
Rút gọn biểu thức:
a/ A=100^2-99^2+98^2-97^2+...+2^2-1^2
b/ B=3(2^2+1)(2^4+1)...!2^64+1)+1
\(A=100^2-99^2+98^2-97^2+....+2^2-1^2\)
\(=\left(100-99\right).\left(100+99\right)+\left(98-97\right).\left(98+97\right)+....+\left(2-1\right).\left(2+1\right)\)
\(=1+2+....+97+98+99+100=\frac{100.\left(100+1\right)}{2}=5050\)
\(B=3\left(2^2+1\right)\left(2^4+1\right)....\left(2^{64}+1\right)+1=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\)
\(=\left(2^4-1\right)\left(2^4+1\right)......\left(2^{64}+1\right)+1=\left(2^8-1\right).....\left(2^{64}+1\right)+1\)
Tiếp tục rút gọn như vậy,ta đc \(B=\left(2^{64}-1\right)\left(2^{64}+1\right)=2^{128}-1+1=2^{128}\)
Thu gọn tổng sau:
a) A=1+3+3^2+...+3^100
b) B=2^100-2^99+2^98-2^97+...+2^2-2
c) C=3^100-3^99+3^98-3^97+...+3^2-3+1
a) A =1+3+32+33+...+3100
3A = 3 + 32+33+...+3101
3A-A=( 3 + 32+33+...+3101)-(1+3+32+33+...+3100)
2A = 3101-1
A = \(\frac{3^{101}-1}{2}\)
Thùy An làm sai rùi
a) A=1+3+3^2+...+3^100
3A=3+3^2+....+3^101
3A-A=1+3^101
A=(1+3^101)/2
a) A=1+3+32+...+3100
3A= 3+32+...+3100+3101
3A-A=3101-1
2A=3101-1
A=(3101-1):2
Tính:
a) A=2^100 - 2^99 + 2^98 - 2^97 + ... + 2^2 - 2
b) B=3^100 - 3^99 + 3^98 - 3^97 + ... + 3^2 - 3
thu gọn các tổng :
A=2^100 - 2^99 +2^98 - 2^97 +...+ 2^2 - 2
B= 3^100 - 3^99 + 3^98 - 3^97 +...+ 3^2 - 3 +1
A = 2100 - 299 + 298 - 297 +...+ 22 - 2
=> 2A = 2101 - 2100+299 - 298+...+23-22
=> 2A+A= 2101 -2
=> \(A=\frac{2^{101}-2}{3}\)
phần B bn lm tương tự nha!
Rút gọn biểu thức
b) B=2^100-2^99+2^98-2^97+...+2^2-2
c) C=3^100-3^99+3^98-3^97+...+3^2-3+1
b) B = 2100 - 299 + 298 - 297 + ...+ 22 - 2
=> B x 2 = 2101 - 2100 + 299 - 298 + ...23 - 22
=> B x 2 + B = (2101 - 2100 + 299 - 298 + ...23 - 22 ) + (2100 - 299 + 298 - 297 + ...+ 22 - 2)
<=> B x 3 = 2101 - 2 = 2. ( 299 - 1)
=> B = \(\frac{2.\left(2^{99}-1\right)}{3}\)
Phần c) Làm tương tự Lấy C x 3 rồi + với C.
Tính nhanh
a, 1-2+3-4+.....+2015-2016+2017
b,1+3-5-7+9+11+....+97-98-99+100+101
c,1-2-3+4+5-6-7+....+97-98-99+100+101
d,2^100-2^99-2^98-....-2-1
Nhanh nha m dang cần gấp
Rút gọn:
a/ A=2^100-2^99+2^98-2^97+............+2^2-2
b/ B=3^100-3^99+3^98-3^97+..............+3^2-3+1
Ai nhanh nhất là đúng nhất mk tick cho
\(A=2^{100}-2^{99}+2^{98}-2^{97}+....+2^2-2\)
\(2A=2^{101}-2^{100}+2^{99}-2^{98}+....+2^3-2^2\)
\(2A+A=2^{101}-2\)
\(A=\frac{2^{101}-2}{3}\)
b) tương tự
\(B=\frac{3^{101}+1}{4}\)
Rút gọn:
a) \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
b) \(B=3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)
A = 2100 - 299 + 298 - 297 + ... + 22 - 2
= ( 2100 + 298 + ... + 22 ) - ( 299 + 297 + ... + 2 )
= ( 2100 + 298 + ... + 22 ) - 2( 299 + 297 + ... + 2 ) + ( 299 + 297 + ... + 2 )
= 299 + 297 + ... + 2
=> 4A = 2103 + 299 + ... + 23
=> 3A = 2103 - 2
=> A = \(\frac{2^{103}-2}{3}\)
Tính giá trị các biểu thức sau:
a) A = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100
b) B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100
a)
C = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = − 1 + − 1 + ... + − 1 + − 1 = − 1.50 = − 50.
b)
B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100 = 1 − 2 + − 3 + 4 + 5 − 6 + ... + 97 − 98 + − 99 + 100 = − 1 + 1 + − 1 + ... + − 1 + 1 = − 1 + 1 + − 1 + 1 + ... + − 1 + 1 − 1 = 0 + 0 + ... + 0 − 1 = − 1.