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Question

For every natural number n(>1), prove that 4n+15n1 is divisible by 9.

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Solution

Proving by induction,
for n=1, 4n+15n1=18
Let for n=k, 4k+15k1=9λ1
for n=kH=4k+1+15(k+1)1
=4.4k+15k+14
=4(9λ1+115k)+15k+14
=36λ1+460k+15k+14=36λ145k+18
=9(4λ15k+2)=9λ1.

1208040_1395146_ans_dc46f5a8e86c4b6ca358cd70bd2e34f0.jpg

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