AP EAMCET202017 Sep 2020Morning ShiftMathematicsBasics of MathematicsActual
( k^5 5 + k^3 3 + 7 15 k ) is if (k N )
Options
- AA natural number
- BAn integer
- CA positive fraction
- DEqual to zero
Correct answer
A. A natural number
Step-by-step solution
Let (P(K)= k^5 5 + k^3 3 + 7 k 15 , k N ) ( gathered = 3 k^5 15 + 5 k^3 15 + (15-5-3) k 15 = 3 15 (k^5-k )+ 5 15 (k^3-k )+k = 1 5 k (k^2+1 )(k+1)(k-1) _ divisible by 5 + 1 3 k(k+1)(k-1) _ divisible by 3 +k gathered ) So, overall it is a natural number.