Question

. Prove that 1+2+3+......+ n is greater than 1/8(2n+1)^2​

Answer 1

Consider

Let the given statement be P(n), i.e.,

P(n): 1 + 2 + 3 + … + n < 1/8(2n+1)2

It can be noted that P(n) is true for n = 1 since .

1<1/8 (2.1 + 1)2 = 9/8

Let P(k) be true for some positive integer k, i.e.,

1 + 2 + 3 + … + k < 1/8(2k+1)2 ————(1)

We shall now prove that P(k+1) is true whenever P(k) is true.

Consider

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Answer 2

Answer:

your answer is in the attachment

Step-by-step explanation:

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