Prove using mathematical induction
2+4+6+......+2n=n²+n
Asked by Www.jasbirkaurmakhija
19th August 2019,
8:46 PM
Answered by Expert
Answer:
P(1):
Let n=1
L.H.S=2
R.H.S=12+1=2
Therefore it is true for n=1
Let us assume that the result is true for n=k
i.e. 2+4+6+...+2k=k2+k
P(k+1): Let n=k+1
LHS=2+4+6+...+2k+2(k+1)
=k2+k+2(k+1) .... Using assumption for n=k
=k2+k+2k+2
=k2+2k+1+k+1
=(k+1)2+k+1
=RHS
Thus, the result is tru for n=k+1
Hence, 2+4+6+...+2n=n2+n is true for all n
N
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Answered by Expert
20th August 2019,
10:35 AM
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