Let f(1) = 1 and f(n) = 2 underset(r=1)o...

Let `f(1) = 1 and f(n) = 2 underset(r=1)overset(n-1)sumf (r)`. Then, `underset(n=1)overset(m) sumf(n)` is equal to

A

`(7n(n+1))/(2)`

B

`(7n)/(2)`

C

`(7(n+1))/(2)`

D

7n(n+1)

Text Solution

Verified by Experts

The correct Answer is:

A

We heve,
`f(x+y)=f(x)f(y)" for all "x,yinR`
`rArr" "f(x)=xf(1)" for all "x inR`
`rArr" "f(x)=7x" for all "x in R`
`:." "underset(r=1)overset(n)sumf(r)=underset(r=1)overset(n)sum7r=7underset(r=1)overset(n)sumr=(7n(n+1))/(2)`

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