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गणितीय आगमन सिद्धांत से सिध्द कीजिए कि न...

गणितीय आगमन सिद्धांत से सिध्द कीजिए कि निम्नलिखित कथन n के सभी धन पूर्णांक मानो के लिए सत्य है ।
`1.4.7 + 2.5.8 + 3.6.9 + ....+n(n+3)(n+6)=(n)/(4)[(n+1)(n+6)(n+7)]`

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Prove 1.4.7+2.5.8+3.6.9+....... upto n terms =(n)/(4)(n+1)(n+6)(n+7)

Prove 1.4.7+2.5.8+3.6.9+....... upto n terms =(n)/(4)(n+1)(n+6)(n+7)

Prove 1.4.7+2.5.8+3.6.9+....... upto n terms =(n)/(4)(n+1)(n+6)(n+7)

Prove 1.4.7+2.5.8+3.6.9+....... upto n terms =(n)/(4)(n+1)(n+6)(n+7)

1.3 + 2.4 + 3.5 + …… + n(n+2) =( n(n+1)(2n+7))/6

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)

1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^(2)+6n-1))/(3)

n if (1)/(4l)+(1)/(5!)+(1)/(6!)=(n)/(7!)

Prove that 1.3+3.5+5.7+......+(2n-1)(2n+1)=(n(4n^2+6n-1))/3

By using the Principle of Mathematical Induction, prove the following for all n in N : 1.4.7+2.5.8+3.6.9+.......+ n(n + 3)(n+ 6)= n/4 (n +1)(n+ 6)(n+ 7) .