Question

by mathematical induction 1.2²+2.3²+.....+n(n+1)(n+2)(3n+5)/12​

Answer 1

Step-by-step explanation:

1.2+2.3+3.4+⋯+n(n+1)=∑k=1nk(k+1)

=∑k=1n(k2+k)

=∑k=1n(k2)+∑k=1n(k)

=n(n+1)(2n+1)6+n(n+1)2

=n(n+1)6(2n+1+3)

=n(n+1)6(2n+4)

=n(n+1)6[2(n+2)]

=n(n+1)(n+2)3