CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

$$f(1)=1,n\geq  1\Rightarrow f(n+1)=2f(n)+1$$ then f(n)=


A
2n+1
loader
B
2n
loader
C
2n1
loader
D
2n11
loader

Solution

The correct option is C $$2^n-1$$
$$f(1)=1$$ $$n\ge 1$$
$$f(n+1)=2f(n)+1\\f(2)=2f(1)+1\\3=2^2-1\\f(3)=2.3+1\\7=2^3-1\\f(4)=2.7+1\\=15 =2^4-1$$
So, $$f(n)=2^n-1$$
Answer C

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image