pl prove this induction quest

Asked by Kirandoon | 27th Aug, 2008, 09:53: PM

Expert Answer:

if n=1 then 52+4.6 = 49 when divided by 20 , remainder is 9 i.e. true for n=1

for n=2 , 53+4.62 = 269 divide by 20 leaves remainder 9, true for n=2

let us assume it is true for n=N i.e. 5N+1 + 4. 6N leaves remainder 9 when divided by 20

now we have to show that it is true for n=N+1

5N+2 + 4. 6N+1 = 5.5N+1+24 . 6N = 5N+1 + 4. 6N+ 20.6N + 4.5N+1 = 5N+1 + 4. 6N+ 20(6N + 5N )

here 20(6N + 5N ) is divisible by 20, so we are left with 5N+1 + 4. 6N which leaves remainder 9 when divided by 20 which is true by our hypothesis.

so this statement is true for all n.

 

Answered by  | 11th Sep, 2008, 10:58: PM

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