计算1/3+1/8+1/15+...+1/120
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计算1/3+1/8+1/15+...+1/120
计算1/3+1/8+1/15+...+1/120
计算1/3+1/8+1/15+...+1/120
1/1*3+1/2*4+1/3*5+.
=1/2(1-1/3+1/3-1/5+.+1/10-1/12)
=1/2(1-1/12)
=11/24
=1/1*3+1/2*4+1/3*5+...+1/10*12
=(1/1*3+1/3*5+...+1/9*11) +(1/2*4+1/4*6+...+1/10*12)
=1/2* (1-1/3+1/3-1/5+...+1/9-1/11) +1/2*(1/2-1/4+1/4-1/6+...+1/10-1/12)
=1/2(1-1/11)+1/2*(1/2-1/12)
=5/11+5/24=175/264
1/3+1/8+1/15+...+1/120
=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(10*12)
=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(9*11)+1/(10*12)
=1/(1*3)+1/(3*5)+...+1/(9*11) + 1/(2*4)+...+1/(10*12)
=1/2 * (1-1/3+1/...
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1/3+1/8+1/15+...+1/120
=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(10*12)
=1/(1*3)+1/(2*4)+1/(3*5)+...+1/(9*11)+1/(10*12)
=1/(1*3)+1/(3*5)+...+1/(9*11) + 1/(2*4)+...+1/(10*12)
=1/2 * (1-1/3+1/3-1/5+...+1/9-1/11 + 1/2-1/4+...+1/10-1/12)
=1/2 * (1-1/11 + 1/2-1/12)
=1/2 * (10/11 + 5/12)
=1/2 * (120 + 55)/(11*12)
= 175 / (2*11*12)
= 175 / 264
收起
用裂项的方法在结合数列就可做出