Q.

If f(1)=1, f(n+1)=2f(n)+1 and n≥1,then f(n) is equal to

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a

.2n+1

b

2n

c

2n.-1

d

2n-1-1

answer is C.

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Detailed Solution

Given ,f(1)=f(n+1)=2f(n)+1,n≥1           f(2)=f(1+1)=2f(1)+1=2*1+1=3=22-1           f(3)=f(2+1)=2f(2)+1=2*3+1=7=23-1           f(4)=f(3+1)=2f(3)+1=2*7+1=15=24-1           f(5)=f(4+1)=2f(4)+1=2*15+1=31=25-1f(n)=f((n-1)+1)=2f(n-1)+1=2n-1
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If f(1)=1, f(n+1)=2f(n)+1 and n≥1,then f(n) is equal to