Cho A=5mũ 50-5 mũ 48+5 mũ 46-5 mũ 44+…+5 mũ 6-5 mũ 4+5 mũ 2-1 17/08/2021 Bởi Autumn Cho A=5mũ 50-5 mũ 48+5 mũ 46-5 mũ 44+…+5 mũ 6-5 mũ 4+5 mũ 2-1
Ta có: A=550-548+546-544+…+56-54+52-1 => 25A=552-550+548-546+…+58-56+54-52 => A+25A=552-1 => 26A=552-1 => A= 5^52-1 26 Bình luận
Đáp án: $A=\dfrac{5^{52}-1}{26}$ Giải thích các bước giải: $A=5^{50}-5^{48}+5^{46}-5^{44}+…+5^{6}-5^{4}+5^{2}-1$ $\rightarrow A=(5^{50}-5^{48})+(5^{46}-5^{44})+…+(5^{6}-5^{4})+(5^{2}-1)$ $\rightarrow A=(5^{2}-1)5^{48}+(5^{2}-1)5^{44}+…+(5^{2}-1)5^{4}+(5^{2}-1)$ $\rightarrow A=(5^{2}-1)(5^{48}+5^{44}+…+5^{4}+1)$ $\rightarrow A=(25-1)(5^{48}+5^{44}+…+5^{4}+1)$ $\rightarrow A=24(5^{48}+5^{44}+…+5^{4}+1)$ $\rightarrow 5^4.A=24(5^{52}+5^{48}+…+5^{8}+5^4)$ $\rightarrow 5^4.A-A=24(5^{52}+5^{48}+…+5^{8}+5^4)-24(5^{48}+5^{44}+…+5^{4}+1)$ $\rightarrow (5^4-1).A=24(5^{52}+5^{48}+…+5^{8}+5^4-(5^{48}+5^{44}+…+5^{4}+1))$ $\rightarrow (625-1).A=24(5^{52}-1)$ $\rightarrow 624.A=24(5^{52}-1)$ $\rightarrow A=\dfrac{5^{52}-1}{26}$ Bình luận
Ta có: A=550-548+546-544+…+56-54+52-1
=> 25A=552-550+548-546+…+58-56+54-52
=> A+25A=552-1
=> 26A=552-1
=> A= 5^52-1
26
Đáp án:
$A=\dfrac{5^{52}-1}{26}$
Giải thích các bước giải:
$A=5^{50}-5^{48}+5^{46}-5^{44}+…+5^{6}-5^{4}+5^{2}-1$
$\rightarrow A=(5^{50}-5^{48})+(5^{46}-5^{44})+…+(5^{6}-5^{4})+(5^{2}-1)$
$\rightarrow A=(5^{2}-1)5^{48}+(5^{2}-1)5^{44}+…+(5^{2}-1)5^{4}+(5^{2}-1)$
$\rightarrow A=(5^{2}-1)(5^{48}+5^{44}+…+5^{4}+1)$
$\rightarrow A=(25-1)(5^{48}+5^{44}+…+5^{4}+1)$
$\rightarrow A=24(5^{48}+5^{44}+…+5^{4}+1)$
$\rightarrow 5^4.A=24(5^{52}+5^{48}+…+5^{8}+5^4)$
$\rightarrow 5^4.A-A=24(5^{52}+5^{48}+…+5^{8}+5^4)-24(5^{48}+5^{44}+…+5^{4}+1)$
$\rightarrow (5^4-1).A=24(5^{52}+5^{48}+…+5^{8}+5^4-(5^{48}+5^{44}+…+5^{4}+1))$
$\rightarrow (625-1).A=24(5^{52}-1)$
$\rightarrow 624.A=24(5^{52}-1)$
$\rightarrow A=\dfrac{5^{52}-1}{26}$