1+2+3+--------+n/1+3+5+------+2n-1=
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(1+2+3+....+n) / (1+3+5+....+2n-1)
= (1+2+3+....+n) / (1+3+5+...2n-1) + (2+4+6+...+2n)
-(2+4+6+...+2n)
= (1+2+3+...+n) / {(1+2+3+...+2n)-2(1+2+3+....+n)}
= (n(n+1)/2) / {(2n(2n+1)/2}- 2n(n+1)/2
= (n(n+1)/2) / n(2n+1)-n(n+1)
= n(n+1)/2 / 2n²+n-n²-n
= n(n+1)/2 / n²
= (n+1)/2n
= (1+2+3+....+n) / (1+3+5+...2n-1) + (2+4+6+...+2n)
-(2+4+6+...+2n)
= (1+2+3+...+n) / {(1+2+3+...+2n)-2(1+2+3+....+n)}
= (n(n+1)/2) / {(2n(2n+1)/2}- 2n(n+1)/2
= (n(n+1)/2) / n(2n+1)-n(n+1)
= n(n+1)/2 / 2n²+n-n²-n
= n(n+1)/2 / n²
= (n+1)/2n
prashanthlucky:
thanks
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