Question

Answer 1

\(B=1+5+5^2+5^3+...+5^{150}\)

\(\Rightarrow5B=5+5^2+...+5^{151}\)

\(\Rightarrow4B=5B-B=5+5^2+...+5^{151}-1-5-5^2-...-5^{150}=5^{151}-1\)

\(\Rightarrow B=\dfrac{5^{151}-1}{4}\)

Answer 2

\(5B=5+5^2+...+5^{151}\)

\(\Leftrightarrow B=\dfrac{5^{151}-1}{4}\)

Answer 3

\(B=1+5+5^2+...+5^{150}\)

\(5B=5+5^2+...+5^{150}+5^{151}\)

\(5B-B=\left(5+5^2+...+5^{151}\right)-\left(1+5+5^2+...+5^{150}\right)\)

\(4B=5^{151}-1\Rightarrow B=\dfrac{5^{151}-1}{4}\)