Răspuns :
S=1+3+3²+.......+3⁵⁰
3S=3+3²+3³+....+3⁵⁰+3⁵¹
------------------------------- (-)
2S=3⁵¹-1
S=(3⁵¹-1)/2
2(1+3+3²+.......+3⁵⁰) < 3⁵¹
2 S < 3⁵¹
2*(3⁵¹-1)/2 < 3⁵¹
3⁵¹-1< 3⁵¹ ( adevarat )
S=1+3+3²+.......+3⁵⁰
3S=3+3²+3³+....+3⁵⁰+3⁵¹
------------------------------- (-)
2S=3⁵¹-1
S=(3⁵¹-1)/2
2(1+3+3²+.......+3⁵⁰) < 3⁵¹
2 S < 3⁵¹
2*(3⁵¹-1)/2 < 3⁵¹
3⁵¹-1< 3⁵¹ ( adevarat )