For-all-n-1-n-Z-prove-that-p-n-4-8-4n-2n-n-1-

Question Number 12209 by tawa last updated on 16/Apr/17

For all n ⩾ 1, n \in Z, prove that,

p (n) : 4 + 8 + \dots + 4 n = 2 n (n + 1)

Commented by tawa last updated on 16/Apr/17

please show me full workings sirs . God bless you all .

Answered by mrW1 last updated on 16/Apr/17

S = 4 + 8 + \dots + 4 n

\frac{S}{4} = 1 + 2 + \dots + n

\frac{S}{4} = n + \dots + 2 + 1

\frac{S}{4} + \frac{S}{4} = (1 + n) + \dots + (n + 1) = n (n + 1)

\frac{S}{2} = n (n + 1)

\Rightarrow S = 2 n (n + 1)

Commented by tawa last updated on 16/Apr/17

i appreciate sir . God bless you .

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