Question

prove by mathematical induction that 1+2+3+.......+n (n+1)/2

Answer 1

can u pls tell me what's "n"

Answer 2

Answer:

Let P(n) be the statement given by

1 + 2 + 3 + ..... n = (n + 1) /2

P(1) = 1 (1 + 1) /2

= 1, True

Let it be true for n = m

1 + 2 + 3 + .... + m = m (m + 1) /2

1 + 2 + 3 + ... + (m + 1) ^2 = m(m + 1) /2 + (m + 1)

P(m + 1) = m(m + 1) /2 + (m + 1)

$p(m + 1) = m {}^{2} + 3m + 2 \div 2$

$p(m + 1) = (m + 1)(m + 2) \div 2$

Thus, P(m) is true =>>> P(m + 1) is True.

Step-by-step explanation:

@SSR