Question #0516e

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Answer 1 · 2017-05-01T18:25:26

Assume true for #n = k#

So:

#T_k = k^2 + k# and #T_k mod 2 = 0#

#T_(k+1) = (k+1)^2 + (k+1) #

# = k^2+3k + 2 #

# = k^2+ k + 2(k + 1) #

# = T_k + color(red)(2)(k + 1) implies T_(k+1) mod 2 = 0#

Now establish for #k =1#

#T_1 = 2 implies T_1 mod 2 = 0#

Therefore by induction #T_(2,3,...) mod 2 = 0#