2n m 1 n n m m n 1 n m now replace m with jn in

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Unformatted text preview: = n +1 n − m ⎠ Now, the first three sums can be turned into a single sum if we pull out one of the redundant m=0 terms ( 1 ) from the first two sums and subtract off the m=n term n ( 21n ) that needs to be added write a single sum, k k 1 ⎛1 1 1 1⎞ − +∑ +∑ ⎜ n 2n ⎟ . 2n ⎝ m = 1− n n + m m = n +1 n − m ⎠ Now, replace m with j ­n in the first sum, k 1 ⎛ 1 1 k+n 1 1⎞ S= − +∑ + ∑ ⎜ n 2n ⎟ . 2n ⎝ j =1 j m = n +1 n − m ⎠ S= Replace m with n+j in the last sum, 1 ⎛ 1 1 k+n 1 k−n...
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