1/2²-1+1/4²-1+1/6²-1+。。。+1/50²-1怎么解，请教高手
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1/（2²-1）+1/（4²-1）+1/（6²-1）+。。。+1/（50²-1）
=1/（1×3）+1/（3×5）+1/（5×7）+……+1/（49×51）
=（1-1/3+1/3-1/5+1/5-1/7+……+1/49-1/51）÷2
=（1-1/51）÷2
=50/51÷2
=25/51
=1/（1×3）+1/（3×5）+1/（5×7）+……+1/（49×51）
=（1-1/3+1/3-1/5+1/5-1/7+……+1/49-1/51）÷2
=（1-1/51）÷2
=50/51÷2
=25/51
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1/2²-1+1/4²-1+1/6²-1+。。。+1/50²-1
=1/(2²-1)+1/(4²-1)+1/(6²-1)+。。。+1/(50²-1)
=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+。。。+1/(49*51)
= [ (3-1)/(1*3)+ (5-3)/(3*5)+(7-5)/(5*7)+(9-7)/(7*9)+。。。+(51-49)/(49*51) ]/2
= [ 1 - 1/3 + 1/3 -1/5 + 1/5 -1/7 + 1/7 -1/9 +... + 1/49 - 1/51 ]/2
=(50/51)/2
=25/51
=1/(2²-1)+1/(4²-1)+1/(6²-1)+。。。+1/(50²-1)
=1/(1*3)+1/(3*5)+1/(5*7)+1/(7*9)+。。。+1/(49*51)
= [ (3-1)/(1*3)+ (5-3)/(3*5)+(7-5)/(5*7)+(9-7)/(7*9)+。。。+(51-49)/(49*51) ]/2
= [ 1 - 1/3 + 1/3 -1/5 + 1/5 -1/7 + 1/7 -1/9 +... + 1/49 - 1/51 ]/2
=(50/51)/2
=25/51
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