SETS

Asked by  | 28th Jun, 2008, 12:23: PM

Expert Answer:

We will prove the result by principle of mathematical induction.

to show, 4n -3n -1= 9(m-1), n,m N

for n=1

4n -3n -1=0=9x0=9(1-1). thus, result is true for n = 1

let the result be true for n = k.

this implies, 4k-3k-1 = 9(m-1) for some m in N

consider n = k+1

4k+1-3(k+1) -1

=4k.4-3k-4-12k+12k

=4(4k-3k-1)+9k

=4.9(m-1)+9k

=9(4m-4+k)

=9(p-1) where p =4m+k-3 N

hence, it is true for all n in N by principle of mathematical induction.

Answered by  | 15th Jul, 2008, 11:33: AM

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