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

\(2A-A=\left(2^2+2^3+...+2^{21}\right)-\left(2+2^2+...+2^{20}\right)\)

\(A=2^{21}-2\)

B tương tự câu A

\(5C-C=\left(5^2+5^3+...+5^{51}\right)-\left(5+5^2+...+5^{50}\right)\)

\(C=\dfrac{5^{51}-5}{4}\)

\(3D-D=3+3^2+...+3^{101}-\left(1+3+...+3^{100}\right)\)

\(D=\dfrac{3^{101}-1}{2}\)

\(A=2^1+2^2+2^3+...+2^{20}\)

\(2\cdot A=2^2+2^3+2^4+...+2^{21}\)

\(A=2^{21}-2\)

\(B=2^1+2^3+2^5+...+2^{99}\)

\(4\cdot B=2^3+2^5+2^7+...+2^{101}\)

\(B=\)\(\left(2^{101}-2\right):3\)

\(C=5^1+5^2+5^3+...+5^{50}\)

\(5\cdot C=5^2+5^3+5^4+...+5^{51}\)

\(C=(5^{51}-5):4\)

\(D=3^0+3^1+3^2+...+3^{100}\)

\(3\cdot D=3^1+3^2+3^3+...+3^{101}\)

\(D=(3^{101}-1):2\)

giải chi tiết ý b ddc ko

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) \(3\cdot3^5\cdot3^4\cdot3^2\)

\(=3^{1+5+4+2}\)

\(=3^{12}\)

4333344

?reeeeeeeeeeee

Ủa, cái số gì đây??????

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

\(\frac{2}{3}\times5+\frac{2}{3}\times7+\frac{2}{3}\times9+\frac{2}{3}\times11+\frac{2}{3}\times13+\frac{2}{3}\times15\)

=\(\frac{2}{3}\)\(\times\)( 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)

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

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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