-2+3=?
Chứng minh rằng:
a) A=1/3+1/(3^2)+1/(3^3)+...+1/(3^99)<1/2
b) B=3/(1^2*2^2)+5/(2^2*3^2)+7/(3^2*4^2)+...+19/(9^2*10^2)<1
c) C=1/3+2/(3^2)+3/(3^3)+4/(3^4)+...+100/(3^100)<3/4
a, Cho biết: \(1^2+2^2+3^2+...+10^2=385\)
Tính A= \(3^2+6^2+9^2+...+30^2\)
b, Cho biết: \(1^3+2^3+3^3+...+10^3=3025\)
Tính B= \(2^3+4^3+6^3+...+20^3\)
a: A=3^2(1^2+2^2+...+10^2)
=9*385
=3465
b: B=2^3(1^3+2^3+...+10^3)
=8*3025
=24200
A= 2+2^2+2^3+...+2^19+2^20
b=2+2^3+2^5+...2^97+2^99
C=5+5^2+5^3+...+5^50
D=1+3+3^2+3^3+...+3^100
\(2A-A=\left(2^2+2^3+...+2^{21}\right)-\left(2+2^2+...+2^{20}\right)\)
\(A=2^{21}-2\)
B tương tự câu A
\(5C-C=\left(5^2+5^3+...+5^{51}\right)-\left(5+5^2+...+5^{50}\right)\)
\(C=\dfrac{5^{51}-5}{4}\)
\(3D-D=3+3^2+...+3^{101}-\left(1+3+...+3^{100}\right)\)
\(D=\dfrac{3^{101}-1}{2}\)
\(A=2^1+2^2+2^3+...+2^{20}\)
\(2\cdot A=2^2+2^3+2^4+...+2^{21}\)
\(A=2^{21}-2\)
\(B=2^1+2^3+2^5+...+2^{99}\)
\(4\cdot B=2^3+2^5+2^7+...+2^{101}\)
\(B=\)\(\left(2^{101}-2\right):3\)
\(C=5^1+5^2+5^3+...+5^{50}\)
\(5\cdot C=5^2+5^3+5^4+...+5^{51}\)
\(C=(5^{51}-5):4\)
\(D=3^0+3^1+3^2+...+3^{100}\)
\(3\cdot D=3^1+3^2+3^3+...+3^{101}\)
\(D=(3^{101}-1):2\)
Rút gọn thành một lũy thừa
a) \(2^5\) . \(2^7\)
b) \(2^3\) . \(2^2\)
c) \(2^4\) . \(2^3\) . \(2^5\)
d) \(2^2\) . \(2^4\) . \(2^6\) . \(2\)
e) \(2\) . \(2^3\) . \(2^7\) . \(2^4\)
f) \(3^8\) . \(3^7\)
g) \(3^2\) . \(3\)
h) \(3^4\) . \(3^2\) . \(3\)
i) \(3\) . \(3^5\) . \(3^4\) . \(3^2\)
nhanh, giải chi tiết thì tớ tick cho
a) \(2^5\cdot2^7\)
\(=2^{5+7}\)
\(=2^{12}\)
b) \(2^3\cdot2^2\)
\(=2^{3+2}\)
\(=2^5\)
c) \(2^4\cdot2^3\cdot2^5\)
\(=2^{4+3+5}\)
\(=2^{12}\)
d) \(2^2\cdot2^4\cdot2^6\cdot2\)
\(=2^{2+4+6+1}\)
\(=2^{13}\)
e) \(2\cdot2^3\cdot2^7\cdot2^4\)
\(=2^{1+3+7+4}\)
\(=2^{15}\)
f) \(3^8\cdot3^7\)
\(=3^{8+7}\)
\(=3^{15}\)
g) \(3^2\cdot3\)
\(=3^{2+1}\)
\(=3^3\)
h) \(3^4\cdot3^2\cdot3\)
\(=3^{4+2+1}\)
\(=3^7\)
I) \(3\cdot3^5\cdot3^4\cdot3^2\)
\(=3^{1+5+4+2}\)
\(=3^{12}\)
Chứng minh rằng:
a,A=1/2+1/2^2+1/2^3+.+1/2^2<1
b,B=1/3+1/3^2+1/3^3+...+1/3^n<1/2
c,B=1/2-1/2^2+1/2^3-1/2^4+...+1/2^2015-1/2^2016<1/3
d,D=1/3+2/3^2+3/3^3+4/3^4+...+100/3^100<3/4
?reeeeeeeeeeee
Ủa, cái số gì đây??????
Điền vào ô vuông các dấu thích hợp (=, <,>)
1^2 ... 1
2^2 ... 1+3
3^2 ...1+3+5
1^3 ... 1^2 - 0^2
2^3 ... 3^2 - 1^2
3^3 ... 6^2 - 3^2
4^3 ... 10^2 - 6^2
(0+1)^2 ... 0^2 + 1^2
(1+2)^2 ... 1^2 + 2^2
(2 + 3)^2 ... 2^3 + 3^2
Lời giải chi tiết
12 1 13
12 – 02 (0 + 1)2
02 +12
22 1 + 3 23
32 – 12 (1 + 2)2
12 + 22
32 1 + 3 + 5 33
62 – 32 (2 + 3)2
22 + 32
43 102 – 62
= , = , = , = , = , > nhé
GHGH3UG TRGGHJg ytg gjgdgfgh ẻughrkhfkjrthgh] ơyt]ơ ươ]y[ươ] ơ]m ơ]ơ] ơu]y[ ưu[y ưuy[ ưu[y] y[ợ]uợ]uợ]uợu]j[u]j[u]j[u]j[u]j[u]j[u]ơu]j[ựu[ụ]uợ]uơ]uợu] uhyiuu5yturyytytyytyytty8ytytytytyty58yt85yt85y8ty85yt85y8ty58yt85yt85yt85y8t5yt8y58ty58yt85yt85yt85y58tyyyr5ybtyurygytbgbrbvtterytiburbyvfudytubertuygtdrtuufutydiytuiydyiuyuityurdyiutyruytiurdyuitiurtuyrdytuiyryritrybtiyryrtiutybbirybtreybruiiurytryvui
2/3*5 + 2/3*7 + 2/3*9 + 2/3*11 + 2/3*13 + 2/3*15
2/1*2 + 2/2*3 + ....................... + 2/9*10
3/1*2 + 3/2*3 + ..........................+ 3/9*10
Giup mk theo kiểu dễ hiểu và đơn giản nhất nhé !
\(\frac{2}{3}\times5+\frac{2}{3}\times7+\frac{2}{3}\times9+\frac{2}{3}\times11+\frac{2}{3}\times13+\frac{2}{3}\times15\)
=\(\frac{2}{3}\)\(\times\)( 5+7+9+11+15)
= \(\frac{2}{3}\)\(\times\)47
= \(\frac{94}{3}\)
Có friend forever II Lê Tiến Đạt giải rồi nhé nên đừng bắt tui giải nữa ( chuồn là thượng sách)
Thực hiện phép tính
a. M=-1^2+2^2-3^2+4^2-...-99^2+100^2.
b. M=-1^3+2^3-3^3+4^3-5^3+6^3-7^3+8^3-2^2-4^2-6^2-8^2.
a. M=-1^2+2^2-3^2+4^2-...-99^2+100^2.
M=(2-1)(2+1)+(4-3)(4+3)+...+(100-99)(100+99)
M=3+7+...+199
=>2M=3+7+...+199+3+7+...+199 (198 số)
=(3+199)+(7+195)+...+(199+3) (99 cặp)
=202.99
=19998
=>M=19998:2=9999
Tính giá trị biểu thức
a, A = (1 - 1/1+2) . (1 - 1/1+2+3) . (1- 1/1+2+3+4) . ... .(1- 1/1+2+...+100)
b, B = (2/3+ 3/4 +...+99/100).(1/2+2/3+...+98/99) - (1/2+2/3+...+99/100).(2/3+3/4+...+98/99)
c, C = \(\frac{3^3+1^3}{2^3-1^3}+\frac{5^3+2^3}{3^3-2^3}+\frac{7^3+3^3}{4^3-3^3}+...+\frac{41^3+20^3}{21^3-20^3}\)
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A= 1 - 2 - 22 - 23 + 24 +...+ 22022 (sửa đề)
= -13 + (24 + 25 + 26 + ... + 22022)
2A = -26 + (25 + 26 + 27 + ... + 22023)
2A - A = -26 + (25 + 26 + 27 + ... + 22023) - [-13 + (24 + 25 + 26 + ... + 22022)]
A = -13 +(22023 - 24)
= 22023 - 29
Vậy...
B = 1 + 3 + 32 + 33 + 34 + ... + 32022
3B = 3 + 32 + 33 + 34 + 35 +...+ 32023
3B - B = 3 + 32 + 33 + 34 + 35 +...+ 32023 - (1 + 3 + 32 + 33 + 34 + ... + 32022)
2B = 32023 - 1
=> B = \(\dfrac{3^{2023}-1}{2}\)
Vậy...
#Ayumu