Asked by assma
prove sum(x)=n(n+1)/2 from x=1 to x=n
Answers
Answered by
Reiny
what you have is
1+2+3+...+n
let S(n) = 1+2+3+...+ (n-2) + (n-1) + n
writing this in reverse order
S(n) = n + (n-1) + (n-2)+ ... + 3+2+1
add them
2S(n) = (1+n) + (2+n-1) + (3+n-2) +...+(3+n-2) + (2+n-1) + (n+1)
= (n/2)(n+1)
or
= n(n+1)/2 , as required
1+2+3+...+n
let S(n) = 1+2+3+...+ (n-2) + (n-1) + n
writing this in reverse order
S(n) = n + (n-1) + (n-2)+ ... + 3+2+1
add them
2S(n) = (1+n) + (2+n-1) + (3+n-2) +...+(3+n-2) + (2+n-1) + (n+1)
= (n/2)(n+1)
or
= n(n+1)/2 , as required
Answered by
assma
thank you Reiny
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