Prove , by mathematical induction , that 5n+1+4.6n when divided by 20 leaves remainder 9 for all n

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answer is given below
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answer is given below

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particle of mass m moving with an initial velocity u collides inelastically with a particle of mass M initially at rest. If the collision is completely inelastic then find (i) the find velocity of combined entity, and (ii) loss in kinetic energy during collision.
 
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use mathematical induction to prove that 5^(n+1) + 4 × 6^n when divided by 20 leaves a remainder 9, for all natural number n
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