prove by principle of mathematical induction that for all n belongs to N.

n²+n is even natural number

  step 1.  put n=1 

  n²   + n  = 1² +1 =2  which is even

  step 2 . let assume result is true for n=k

  then k² +k is even number

  steo 3. to prove for n=k+1

  (k+1)² + (k+1)

  =  k² + 1 + 2k + k + 1

  =  k² + k + (2k +2)

  i.e = even number + 2 (k+1)  [using 1 . & 2(k+1) is also even   ]

(also an even for all n belomgs to  N)

  therefore  result is true for for all n belongs to N