Find the natural number a for which sum(...

Find the natural number `a` for which `sum_(k=1)^nf(a+k)=16(2^n-1),` where the function `f` satisfies the relation `f(x+y)=f(x)f(y)` for all natural number `x , ya n d ,fu r t h e r ,f(1)=2.`

Verified by Experts

The correct Answer is:

3

FUNCTIONS
VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE)|13 Videos
DIFFERENTIAL EQUATIONS
VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 Videos
INTEGRAL CALCULUS - 2
VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

Similar Questions

Explore conceptually related problems

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

If a real polynomial of degree n satisfies the relation f(x)=f(x)f''(x)"for all "x in R" Then "f"R to R

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

A continuous function f(x)onR->R satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAAx ,y in R Then find f(x)dot

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to