Question

tính tổng

S = \(1+7\) +\(^{7^2}+^{7^3}+....+^{7^{50}}\)

Answer 1

\(S=1+7+7^2+......+7^{50}\)

\(\Leftrightarrow7S=7+7^2+......+7^{50}+7^{51}\)

\(\Leftrightarrow7S-S=\left(7+7^2+.....+7^{51}\right)-\left(1+7+....+7^{50}\right)\)

\(\Leftrightarrow6S=7^{51}-1\)

\(\Leftrightarrow S=\frac{7^{51}-1}{6}\)

Answer 2

\(S=1+7+7^2+7^3+...+7^{50}\\ 7S=7+7^2+7^3+7^4+...+7^{51}\\ 7S-S=7^{51}-1\\ \Rightarrow S=\frac{7^{51}-1}{6}\)