Question

mathematical induction 1+2+3+....+n=1/2(n+1) prove that (answer assignment)

Answer 1

Given that, 1+2+3+........+n=n(n+1)/2......(1)

checking that p(1) is true.

then assume, p(k) is true:

1+2+3+....+k=k(k+1)/2

then check p(k+1) is true:

take LHS of the equ:

1+2+3+......+k+(k+1)=(k(k+1)/2)+(k+1)
{........................ .......=>[(1+2+3+...+k)+(k+1)]}

=k(k+1)/2+(k+1)

=(k^2+k+2k+2)/2

=(k^2+3k+2)/2 [:.k^2+3k+2=(k+1)(k+2)]

=(k+1)(k+2)/2//

so, p(k+1) is true.

and so, by the mathematical induction, we know that p(n) is true for every n£N.