Question

A= 1+2 mũ 2+2 mũ 3 +...+2 mũ 100

Tính tổng

Answer 1

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

\(2A=2+2^3+2^4+...+2^{101}\)

\(2A-A=\left(2+2^3+2^4+...+2^{101}\right)-\left(1+2^2+2^3+...+2^{100}\right)\)

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

B tự tính A nhé 

Answer 2

\(2A=2+2^3+2^4+...+2^{101}\)

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

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

\(A=2+2^{101}-5\)

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

Answer 3

Tính tổng : 

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

2A = 2 + 2^3 + 2^4 +... +2^101

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

A =  ( 2 + 2^101 ) - ( 1 + 2^100 )

    = 2 +  2^101 - 1 + 2^100

    = ( 2 - 1 ) + ( 2^101 + 2^100 )

    =   1 + ( 2^101 + 2^100 )