作业帮1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
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1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.1/49*1/51等于多少,
1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(2n+1)
=1/2[1/1-1/3+1/3-1/5+1/5-1/7+.+1/49-1/51+...+1/(2n-1)-1/(2n+1)]
=1/2[1-1/(2n+1)]
=n/(2n+1)
当n=25时,
1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51+...+1/(2n-1)(2n+1)
=1/1*1/3+1/3*1/5+1/5*1/7+.+1/49*1/51
=25/51
1/1*1/3+1/3*1/5+1/5*1/7+.........1/49*1/51
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.........1/2(1/49-1/51)
=1/2(1-1/3+1/3-1/5+1/5-1/7+.........+1/49-1/51)
=1/2(1-1/51)
=49/102