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Prove using mathematical induction: 5 2n+1 *2 n+2 + 3 n+2 *2 2n+1 is divisible by 19

Prove using mathematical induction: 52n+1*2n+2 + 3n+2*22n+1 is divisible by 19

Grade:12

1 Answers

Vikas TU
14149 Points
4 years ago
Dear student 
Dear student
5^(2n+1)*2^(n+2) + 3^(n+2)*2^(2n+1) is divisible by 19
Put n =1 and check  
Yes it is divisible by 19 
Put n = k 
5^(2k+1)*2^(k+2) + 3^(k+2)*2^(2k+1) = 19J 
Put n = k+1 
5^(2k+3)*2^(k+3) + 3^(k+3)*2^(2k+3) 
=> 25*4*5^(2k+1)*2^(k+2) + 3*4* 3^(k+2)*2^(2k+1) 
100*5^(2k+1)*2^(k+2) + 12*3^(k+2)*2^(2k+1) 
which is divisible by 19 
Hence prooved 
 

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