Question

初一数学题1乘以3分之1加3乘以5分之1加5乘以7分之1.2N减1乘以2N加1分之1是不是得2N加1分之N课老师的答案却

Answer 1

1/(1*3)= (1-1/3)/2

1/(3*5)= (1/3-1/5)/2

1/(5*7)= (1/5-1/7)/2

.

1/[(2N-1)(2N+1)]= [1/(2N-1)-1/(2N+1)]/2

所以

1乘以3分之1加3乘以5分之1加5乘以7分之1.2N减1乘以2N加1分之1

=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+.+[1/(2N-1)-1/(2N+1)]/2

=[1-1/3+1/3-1/5+1/5-1/7+.+1/(2N-1)-1/(2N+1)]/2

=[1-1/(2N+1)]/2

=[2N/(2N+1)]/2

=N/(2N+1)

你的答案正确!