find the sum of the following ( 1-1/n)+(1-2/n)+(1-3/n)+....up to n terms
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Heya user,
[ 1 - 1/n ] + [ 1 - 2/n ] + [ 1 - 3/n ] + ....
= [ n times 1 ] - [ 1 + 2 + 3 + ... ]/n
= n - [ n ( n - 1 ) / 2n ]
= n - [ n - 1 ]/2
= [ 2n - n + 1 ] /2 = [ n + 1 ]/2 <--- Desired Result
[ 1 - 1/n ] + [ 1 - 2/n ] + [ 1 - 3/n ] + ....
= [ n times 1 ] - [ 1 + 2 + 3 + ... ]/n
= n - [ n ( n - 1 ) / 2n ]
= n - [ n - 1 ]/2
= [ 2n - n + 1 ] /2 = [ n + 1 ]/2 <--- Desired Result
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