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Evaluate the expression f left parenthesis n plus 2 right parenthesis minus f left parenthesis n right paren given that f left paren n right paren equals 1 over 2 n left paren n plus 2 right paren?
Starcoke724
A very good try, but f(n) is still ambiguous. I assume you mean
f(n) = 1/2*n*(n+2) and not 1/[2*n*(n+2)]
Then f(n+2) - f(n) = 1/2*(n+2)*(n+2+2) - 1/2*n*(n+2)
= 1/2*(n+2)*(n+4) - 1/2*n*(n+2)
= 1/2*(n+2)*{(n + 4) - n}
= 1/2*(n+2)*4
= 2*(n+2)
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∙ 9y ago
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