Question

Tính tổng

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

Answer 1

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)

Answer 2

A = 1 + 3 + 3² + ... + 3¹⁰⁰

3A = 3 + 3² + 3³ + ... + 3¹⁰¹

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

Answer 3

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

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

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

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

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