Toán Lớp 7: Tính S=1+1/5+1/5^2+…+1/5^n(n thuộc N*)
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Toán Lớp 7: Tính S=1+1/5+1/5^2+…+1/5^n(n thuộc N*)
Comments ( 2 )
S=1+1/5+1/5²+…+1/5^n
⇒5S=5+1+1/5+1/5²+…+1/5^n-1
⇒5S-S=5-1/5^n
⇒4S=5-1/5^n
⇒S={5-\frac{1}{5^n}}/4
S=1+1/5+1/(5^2)+…+1/(5^n)(n∈NN*)
<=>5S=5+1+1/5+1/(5²)+…+1/(5^(n-1))
<=>5S-S=5-1/(5^n)
<=>4S=5-1/(5^n)
<=>S=(5-1/(5^n))/4