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snow_tiger [21]
3 years ago
6

This is for pre-calc can someone pls help

Mathematics
1 answer:
stepladder [879]3 years ago
4 0

Answer:

Question 18: 453,600

Step-by-step explanation:

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For the given statement Pn, write the statements P1, Pk, and Pk+1.
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Answer:

P_{1} =  2

P_{k} = k(k+1)

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Step-by-step explanation:

We are given the statement,

P_{n} as 2 + 4 + 6 + . . . + 2n = n(n+1)

That is,

P_{n} as 2 + 4 + 6 + . . . + 2n = \sum_{i=1}^{n}2i

So, we have,

P_{1} = \sum_{i=1}^{1}2i = 2

P_{k} = \sum_{i=1}^{k}2i = 2 + 4 + 6 + . . . + 2k = k(k+1)

P_{k+1} = \sum_{i=1}^{k}2i = 2 + 4 + 6 + . . . + 2k + 2(k+1) = (k+1)(k+2)

Thus, we get,

P_{1} =  2

P_{k} = k(k+1)

P_{k+1} = (k+1)(k+2)

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