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Prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers​

User Rkagerer
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Answer:

Proved

Explanation:

Given


a_n = 2n

Required

Prove that
S_n = n(n+1)

The given sequence is an arithmetic sequence.

The Sn of this sequence is:


S_n = (n)/(2)(a_1 + a_n)

Calculate a1


a_n =2n


a_1 =2*1


a_1 =2

So, we have:


S_n = (n)/(2)(a_1 + a_n)


S_n = (n)/(2)(2 + 2n)

Factor out 2


S_n = (n*2)/(2)(1 + n)


S_n = n(1 + n)


S_n = n(n + 1) --- Proved

User Omaris
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