a, 1+2 + $2^{2}$ +$2^{3}$ + $2^{4}$ +... + $2^{50}$
Đặt A = 1+2 + $2^{2}$ +$2^{3}$ + $2^{4}$ +... + $2^{50}$
⇔ 2A = 2+$2^{2}$ +$2^{3}$ +$2^{4}$+$2^{5}$ +...+$2^{51}$
⇔ 2A - A= (2+2²+...+$2^{51}$) - (1+2+...+$2^{50}$)
⇔ A = $2^{51}$ - 1
Vậy 1+2 + $2^{2}$ +$2^{3}$ + $2^{4}$ +... + $2^{50}$ = $2^{51}$ - 1
b, 5 + $5^{3}$ + $5^{5}$ + ... +$5^{49}$
Đặt B = 5 + $5^{3}$ + $5^{5}$ + ... +$5^{49}$
⇔ 25B = $5^{3}$ + $5^{5}$ + $5^{7}$ ... +$5^{51}$
⇔ 25B-B = ($5^{3}$ + $5^{5}$ +... + $5^{51}$) - (5 + $5^{3}$ + ... + $5^{49}$)
⇔ 24B = $5^{51}$ - 5
⇔ B = $\frac{5^{51}-5}{24}$
Vậy 5 + $5^{3}$ + $5^{5}$ + ... +$5^{49}$ = $\frac{5^{51}-5}{24}$
