Question

rút gon tổng sau

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

giúp mik nha các bạn......^-^

Answer 1

A*3=(1+3+3²+3³+3⁴+...+3⁹⁹+3¹⁰⁰)

3A=3+3²+3³+3⁴+3⁵+...+3¹⁰⁰+3¹⁰¹

3A-A=(3+3²+3³+3⁴+3⁵+...+3¹⁰⁰+3¹⁰¹)-(1+3+3²+3³+3⁴+...+3⁹⁹+3¹⁰⁰)

2A=3¹⁰¹-1

A=(3¹⁰¹-1):2

Answer 2

A = 1 + 3 + 3² + ... + 3⁹⁹ + 3¹⁰⁰
3A = 3 + 3² + 3³ + ... + 3⁹⁹ + 3¹⁰⁰
3A - A = ( 3 + 3² + 3³ + ... + 3⁹⁹ + 3¹⁰⁰ ) - ( 1 + 3 + 3² + ... + 3⁹⁹ + 3¹⁰⁰ )
2A = 3¹⁰⁰ - 1 
A = \(\frac{3^{100}-1}{2}\)