Question

2. MATHEMATICAL INDUCTION
Let S(K)=1+3+5+...+(2K - 1) = K² +3.
Then which of the following is true?
1) S(1) is correct 2)$(K)= S(K +1)
3) S(K) = S(K +1)
4) P.OF.M.I can be used to prove the
formula​

Answer 1

Answer:

11th

Maths

Principle of Mathematical Induction

Introduction to Mathematical Induction

Let S(K) = 1 + 3 + 5... + (...

MATHS

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Asked on December 27, 2019 by

Khusbu Bhargava

Let S(K)=1+3+5...+(2K−1)=3+K

2

. Then which of the following is true

MEDIUM

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ANSWER

S(k)=1+3+5+...+(2k−1)=3+k

2

S(1)=1=3+1, which is not true

∵ S(1) is not true.

∴ P.M. 1 cannot be applied

Let S(k) is true, i.e.

1+3+5....+(2k−1)=3+k

2

⇒1+3+5....+(2k−1)+2k+1

=3+k

2

+2k+I=3+(k+1)

2

∴S(k)⇒S(k+1