CBSE Class 11-science Answered

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. 5^N+1 + 4. 6^N leaves remainder 9 when divided by 20

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

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

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

so this statement is true for all n.