求解高中通项公式7,77,777,7777;0,根号2,0,根号2;求解这俩个通项公式
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求解高中通项公式7,77,777,7777;0,根号2,0,根号2;求解这俩个通项公式
求解高中通项公式
7,77,777,7777;
0,根号2,0,根号2;求解这俩个通项公式
求解高中通项公式7,77,777,7777;0,根号2,0,根号2;求解这俩个通项公式
an = (7/9)(10^n - 1)
an = [1 + (-1)^n]/√2
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S = 7 + 77 + 777 + 7777 + ...
= 7(1 + 11 + 111 + 1111 + ...)
= 7[(10 - 1)/9 + (100 - 1)/9 + (1000 - 1)/9 + (10000 - 1)/9 + ...]
= (7/9)[(10^1 - 1) + (10^2 - 1) + (10^3 - 1) + (10^4 - 1) + ...]
= Σ (7/9)(10^n - 1)
S = 0 + √2 + 0 + √2 + 0 + √2 + 0 + √2 + ...
= 0 + 2/√2 + 0 + 2/√2 + ...
= (1 - 1)/√2 + (1 + 1)/√2 + (1 - 1)/√2 + (1 + 1)/√2 + ...
= [1 + (-1)^1]/√2 + ([1 + (-1)^2]/√2 + [1 + (-1)^3]/√2 + [1 + (-1)^4]/√2 + ...
= Σ [1 + (-1)^n]/√2
第一个:7×[(1-10^n)/(-9)]
第二个:=(√2/2) × [(-1)^n +1]