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1/(2*5)+1/(5*8)+.+1/(3n-1)(3n+2)=n/6n+4howtoprovebymathematicinduction?
题目详情
1/(2*5)+1/(5*8)+.+1/(3n-1)(3n+2)=n/6n+4
how to prove by mathematic induction?
how to prove by mathematic induction?
▼优质解答
答案和解析
1/（2*5）+1/（5*8）+1/（8*11）+.+1/（(3n-1)(3n+2)
=1/3*(1/2-1/5)+1/3*(1/5-1/8)+.+1/3(1/(3n-1)-1/(3n+2))
=1/3(1/2-1/5+1/5-1/8+1/8-.+1/(3n-1)-1/(3n+2))
=1/3*(0.5-1/(3n+2)
=n/(6n+4)
综上对于任意正整数n上述等式成立.
=1/3*(1/2-1/5)+1/3*(1/5-1/8)+.+1/3(1/(3n-1)-1/(3n+2))
=1/3(1/2-1/5+1/5-1/8+1/8-.+1/(3n-1)-1/(3n+2))
=1/3*(0.5-1/(3n+2)
=n/(6n+4)
综上对于任意正整数n上述等式成立.
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