等比数列an的各项均为正数,(2a4),(a3),(4a5)成等差数列,且a3=2a2^2:(1)求数列an的)求数列an的通项公式(2)求数列an的通项公式(2)设bn=[(2n+5)/(2n+1)(2n+3)]an求数列bn的前n项和sn
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![等比数列an的各项均为正数,(2a4),(a3),(4a5)成等差数列,且a3=2a2^2:(1)求数列an的)求数列an的通项公式(2)求数列an的通项公式(2)设bn=[(2n+5)/(2n+1)(2n+3)]an求数列bn的前n项和sn](/uploads/image/z/11478272-32-2.jpg?t=%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97an%E7%9A%84%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%BA%E6%AD%A3%E6%95%B0%2C%282a4%29%2C%28a3%29%2C%284a5%29%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E4%B8%94a3%3D2a2%5E2%3A%281%29%E6%B1%82%E6%95%B0%E5%88%97an%E7%9A%84%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97an%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97an%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E8%AE%BEbn%3D%5B%282n%2B5%29%2F%282n%2B1%29%282n%2B3%29%5Dan%E6%B1%82%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8Csn)
等比数列an的各项均为正数,(2a4),(a3),(4a5)成等差数列,且a3=2a2^2:(1)求数列an的)求数列an的通项公式(2)求数列an的通项公式(2)设bn=[(2n+5)/(2n+1)(2n+3)]an求数列bn的前n项和sn
等比数列an的各项均为正数,(2a4),(a3),(4a5)成等差数列,且a3=2a2^2:(1)求数列an的)求数列an的通项公式(2
)求数列an的通项公式(2)设bn=[(2n+5)/(2n+1)(2n+3)]an求数列bn的前n项和sn
等比数列an的各项均为正数,(2a4),(a3),(4a5)成等差数列,且a3=2a2^2:(1)求数列an的)求数列an的通项公式(2)求数列an的通项公式(2)设bn=[(2n+5)/(2n+1)(2n+3)]an求数列bn的前n项和sn
等比数列an的各项均为正数
an>0
a1≠0,公比q>0
(2a4),(a3),(4a5)成等差数列
2a3=2a4+4a5
2a1*q^2=2a1*q^3+4a1*q^4
解得
q=1/2或q=-1(舍去)
a3=2a2^2
a1*q^2=2a1^2*q^2
解得
a1=1/2
数列an的通项公式
an=2^(-n)
求数列bn的前n项和sn
用列项求和法求解
bn=[(2n+5)/(2n+1)(2n+3)]an
bn=[2/(2n+1)-1/(2n+3)]*2^(-2)
bn=1/(2n+1)*2^(1-n)-1/(2n+3)*2^(-n)
b1=1/3-1/5*2^(-1)
b2=1/5*2^(-1)-1/7*2^(-2)
b3=1/7*2^(-2)-1/9*2^(-3)
…………………
bn-1=1/(2n-1)*2^(2-n)-1/(2n+1)*2^(1-n)
bn=1/(2n+1)*2^(1-n)-1/(2n+3)*2^(-n)
累加得
sn=1/3-1/(2n+3)*2^(-n)
解毕