1.Let n=11 (1+1)(1+5)12 which is divisible by 32.n=mm (m+1)(m+5) =3x (m+5)=3x/m(m+1)…………………………………………13.n=m+1(m+1)(m+2)(m+5)3x/m (m+1)×(m+1)(m+2)hence divisible by 3
Roma Obaid Gopal
Asked: 2 years ago20221031T20:27:05+05:30
20221031T20:27:05+05:30In: Class 11
n(n+1)(n+5) is a multiple of 3
n(n+1)(n+5) is a multiple of 3
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Monica Edwin
Asked: 2 years ago20221030T05:11:47+05:30
20221030T05:11:47+05:30In: Class 11
n(n+1) (n+5) is a multiple of 3
n(n+1) (n+5) is a multiple of 3
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Leave an answer

for P(1)= 1 2×6=12 which is multiple of 3 It is true then For P(K) = K(k+1) (k+5)=(k2+k) (k+5)=k3+5k2+k2+5kk3+6k2+5k =3m (where m is an integer)k3= 3m6k25kNow for P(k+1)= K+1(k+2)(k+6)=on multiplying we getk3+9k2+20k+12put k3= 3m6k25k3m6k25k+9k2+20k+123(mk2+5k+4) Hence P(k+1) is true And where n ~ natural no.
Yes