Hello, mathshelpneeded!

Deduce that:

. . n . . . . .1 . . . . . . . . . . . . . . .1

. . ∑ .---------------- . = . ½ [1 - ------ ]

. k=1 (2k-1)(2k+1). . . . . . . . . 2n+1

. . . . . . . . .1 . . . . . . . . . . . . .1 . . . . .1

Hint: .---------------- . = . ½ [ ------- - -------- ]

. . . . .(2k-1)(2k+1) . . . . . . . 2k - 1 . 2k + 1

This is a "telescoping" series.