Question 1039512
The sum of ALL the integers from 1 to n
is given by:
{{{ S = ( n*( n+1 )) / 2 }}}
If {{{ n = 101 }}},
{{{ S = ( 101*102 ) / 2 }}}
{{{ S = 10302/2 = 5151 }}}
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The sum of the ODD integers from 1 to n?
I notice that
{{{ 1 = 1 }}}
{{{ 1 + 3 = 4 }}}
{{{ 1 + 3 + 5 = 9 }}}
{{{ 1 + 3 + 5 + 7 = 16 }}}
Let {{{ k }}} = the number of odd integers from 1 to n
So, {{{ S[odd] = k^2 }}}
The are {{{ 51 }}} odd integers in 1 - 101 sequence
{{{ k^2 = 51^2 }}}
{{{ S[odd] = 2601 }}}
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{{{ S[even] = S - S[odd] }}}
{{{ S[even] = 5151 - 2601 }}}
{{{ S[even] = 2550 }}}
Hope I got it!