Question

1/1X3+1/3X5+1/5X7+......+1/17X19+1/19X21 等于多少？为什么

虚心请教 我急等

Answer 1

1/1X3+1/3X5+1/5X7+......+1/17X19+1/19X21 =(2/1X3+2/3X5+2/5X7+......+2/17X19+2/19X21 )÷2=(1/1-1/3+1/3-1/5+1/5-1/7+.............+1/17-1/19+1/19-1/21)÷2=（1-1/21)÷2=10/21

Answer 2

1/1X3+1/3X5+1/5X7+......+1/17X19+1/19X21 =1/2*（1-1/3+1/3-1/5+1/5-1/7+......+1/17-1/19+1/19-1/21)=1/2*(1-1/21)=1/2*(20/21)=10/21.

Answer 3

列项公式：1/1X3=1/1-1/31/3X5=1/3-1/5......原式=1/1-1/3+1/3-1/5+1/5-1/7。。。。。+1/17-1/19+1/19-1/21=1-1/21=20/21

Answer 4

1/1x3+1/3x5+1/5x7+……+1/17x19+1/19x21

=1/2 *(1-1/3+1/3-1/5+......+1/17-1/19+1/19-1/21)

=1/2*(1-1/21)

=10/21