a/ Ta có:
\(5A=5^2+5^3+...+5^{21}\)
\(\Rightarrow5A-A=\left(5^2+5^3+...+5^{21}\right)-\left(5+5^2+...+5^{20}\right)\)
\(\Rightarrow4A=5^{21}-5\)
\(\Rightarrow A=\dfrac{5^{21}-5}{4}\)
b/ D ở đâu thế???
a) Ta có:
A = 5 + 52 + 53 +.....+ 520
5A = 5(5 + 52 + 53 +.....+ 520)
5A = 52 + 53 +.....+ 520 + 521
5A - A = (52 + 53 +.....+ 520 + 521) - (5 + 52 + 53 +.....+ 520)
4A = 521 - 5
A = (521 - 5) : 4
b) Ta có:
A = 5 + 52 + 53 +.....+ 520
= 5 + 52 + (53 + 54 + 55) + (56 + 57 + 58) +....+ (518 + 519 + 520)
= 30 + 53(1 + 5 + 52) + 56(1 + 5 + 52) +....+ 518(1 + 5 + 52)
= 30 + 53.31 + 56.31 +...+ 518.31
= 30 + (53 + 56 +....+ 518) . 31
Vậy số dư khi chia D cho 31 là 30
