Ta có:
\(K=1+5^2+5^3+...+5^{100}\)
\(\Rightarrow5K=5+5^3+5^4+...+5^{101}\)
\(\Rightarrow5K-K=5+5^3+5^4+...+5^{101}-1-5^2-5^3-...-5^{100}\)
\(\Rightarrow4K=5^{101}-4\)
\(\Rightarrow K=\frac{5^{101}-4}{4}\)
Ta có K = 1 + 52 + 54 + 56 + ... + 5100
=> 52.K = 25K = 52 + 54 + 56 + 58 + ... + 5102
Khi đó 25K - K = (52 + 54 + 56 + 58 + ... + 5102) - (1 + 52 + 54 + 56 + ... + 5100)
=> 24K = 5102 - 1
=> K = \(\frac{5^{102}-1}{24}\)
Vậy K = \(\frac{5^{102}-1}{24}\)
