Question

S=1+2+2 la puterea2+2 la puterea3 +.....+2la puterea99+2 la puterea100​

Answer 1

S = 1 + 2 + 2² + .. 2¹⁰⁰

inmultim relatia cu 2

2S = 2 + 2² + 2³ + .. + 2¹⁰¹

adunam si scadem 1

2S = (1 + 2 + 2² + .. + 2¹⁰⁰) + 2¹⁰¹ - 1

in paranteza avem acum S (suma initiala)

scadem S din 2S

2S - S = (1 + 2 + 2² + .. + 2¹⁰⁰) + 2¹⁰¹ - 1 - (1 + 2 + 2² + .. + 2¹⁰⁰)

S = 2¹⁰¹ - 1