+4*5 đó, ủng hộ tui nha

A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100

3 x A = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + ... + 99 x 100 x ( 101 - 98 )

3 x A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ... + 99 x 100 x 101 - 98 x 99 x 100

3 x A = 99 x 100 x 101 = 999900

A = 999900 : 3 = 333300

A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100

A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3

A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)

A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}\)    ( 1 )

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)( 2 )

Lấy ( 2 ) - ( 1 ) ta được :

\(2A=1-\frac{1}{3^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{3^{100}}}{2}\)

bai toan nay kho qua

A=1+3+3^2+3^3+...+3^100

3A=(1+3+3^2+3^3+...+3^100).3

3A=3+3^2+3^3+3^4+...+3^101

3A-A=(3+3^2+3^3+3^4+...+3^101)-(1+3+3^2+3^3+...+3^100)

2A=3^101-1

A=\(\frac{3^{101}-1}{2}\)

( Dấu . là dấu nhân đấy nha)

A = 1 + 3 + 3² + ... + 3¹⁰⁰

3A = 3 + 3² + 3³ + ... + 3¹⁰¹

3A - A = 2A = 3¹⁰¹ - 1
A = \(\frac{3^{101}-1}{2}\)

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

\(3A=3+3^2+........+3^{101}\)

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

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

\(A=\frac{3^{101}-3}{2}\)

\(\Rightarrow3.A=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\)

\(\Rightarrow3.A-A=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{99}}+\frac{1}{3^{100}}\right)\)

\(2.A=1-\frac{1}{3^{100}}=\frac{3^{100}-1}{3^{100}}\Rightarrow A=\frac{3^{100}-1}{2.3^{100}}\)