Question

S=1+2mũ 2+2mũ4+2mũ6+............+2mũ 100

Answer 1

S = 2^0 + 2^2 + 2^4 +...+ 2^100

4S = 2^2 + 2^4 + 2^6 + ... + 2^100 + 2^102

4S - S = 2^2 + 2^4 + 2^6 + ... + 2^100 + 2^102 - ( 2^0 + 2^2 + 2^4 +...+ 2^100 )

3S = 2^102 - 1

S = ( 2^102 - 1 ) / 3