B=1+3+3²+...+3¹⁰⁰

=>B=3⁰+3¹+3²+....+3¹⁰⁰

=>3B=3.(3⁰+3¹+3²+....+3¹⁰⁰)

=>3B=3¹+3²+3³+.....+3¹⁰¹

=> 3B-B=(3¹+3²+3³+....+3¹⁰¹)-(3⁰+3¹+3²+...+3¹⁰⁰)

=>2B = 3¹⁰¹-3⁰

=>2B = 3¹⁰¹-1

=>B= \(\frac{3^{101}-1}{2}\)

C=4 + 4² + 4³ +....+ 4ⁿ

=> C= \(4^1+4^2+4^3+...+4^n\)

=>4C = 4. ( 4¹+4²+4³+...+4ⁿ)

=>4C = 4²+4³+4⁴+....+4ⁿ⁺¹

=>4C-C = (4²+4³+4⁴+....+4ⁿ⁺¹)-(4¹+4²+4³+....+4ⁿ)

=>3C=4ⁿ⁺¹-4¹

=>3C=4ⁿ⁺¹-4

=>C=\(\frac{4^{n+1}-4}{3}\)