deduce that
that the n sum of 1/((2k-1)(2k+1)) = 1/2(1-1/(2n+1))
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.