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If `f:R to R ` satisfies f(x+y)=f(x)+f(y), for all x, y `in` R and f(1)=7, then `sum_(r=1)^(n)f( r)` isA. `(7n)/(2) `B. `(7(n+1))/(2)`C. `7n(n+1) `D. `(7n(n+1))/(2)` |
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Answer» D f(x+y)=f(x)+f(y) ltbgt Put x-1,y=1 `implies` f(2)=2`*`f(1)=2.7 Similarly f(3)=3.7 and so on `sum_(r=1)^(n)f(r)=7(1+2+3+......+n)=(7n(n+1))/(2)` |
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