Question

Prove by induction, where n is a positive integer that 2 2*3 n(n+1) n+1

Answer 1

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page Solution: we want show that 285 280 4x5 nanti hti use prowse this meant by using mathematical induction Step 1 : for n=1, his positive integer Resut is true for n=1 Step 22 we assume that the rest is true for n=k akan 1 2 + x + KCk4 - 1 Kckt) kti kte CAOS 3 13. Now we want to show that result is na K41

classmate Pogle Date Page consider holes, Page 3 that}+ckxDCkte) 4x2 2x3 KCK+) CK+1) CCK +1 +1 (+) CK+DCK+2) K+) CK+1) CK+2) - KCK+2) D (KAZ) CKA) (K+2) (kt (k+2) = k ck +2) +) CKA (k+2) K²+Zk ti CK+i) Ck +2) CK+D CK+) (x+2) L.H.5 kt) Kt2 Now, consider RHS - (x+1)+1 - 1 - 1 (x+2) K+2 -1 ktz ask +2 ) R.His K+) = from equ 4 © - L.H.S= R.H.S. Reout is true for n=ktl. by mathematical induction i Result is true for n-
hence prove .