Question

Find the sum of the series

2 + 5 + 8 ......... + (3*n-1)

write step-by-step algorithm only ( no code)​

Answer 1

Explanation:

Let P(n) be true for n=m, that is, we suppose that

P(m)=2+5+8+11+...+(3m−1)=

2

1

m (3m + 1)

Now P(m + 1) = P(m) + T

m+1

=

2

1

m(3m+1)+[3(m+1)−1]

=

2

1

[3m

2

+m+6m+6−2]

=

2

1

[3m

2

+7m+4]

=

2

1

(m+1)(3m+4)

=

2

1

(m+1)[3(m)+1]

Above relation shows that P(n) is true for n = m + 1.

Also when n = 1,P(n) = 2 =

2

1

(3⋅1+1)

n = 2, (P(n) = 2 + 5 = 7 =

2

1

⋅2(3⋅2+1)