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Strike441 [17]
3 years ago
10

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

Mathematics
2 answers:
fredd [130]3 years ago
8 0
P(n):2+4+6+\cdots+2n=\displaystyle\sum_{i=1}^n2i

P(1):\displaystyle\sum_{i=1}^12i=2=1(1+1)=2

P(k):\displaystyle\sum_{i=1}^k2i=2+\cdots+2k=k(k+1)

P(k+1):\displaystyle\sum_{i=1}^{k+1}2i=2+\cdots+2k+2(k+1)=(k+1)(k+2)
Leno4ka [110]3 years ago
7 0

Answer:

P_{1} =  2

P_{k} = k(k+1)

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

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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In the problem it is already given that Weston Laundry washed 285.38 pounds of towel and 353.47 pounds of sheets from local hotels in 1 day. Firstly we have to find the total pounds of linens that Weston Laundry has washed in 7 days. Then only will it be possible to find the amount of linen washed in a day.
Then t
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4 0
3 years ago
Need Help!
Nezavi [6.7K]

Answer:

fraction 1 and 3 over 5

Step-by-step explanation:

2:3 is equal to 8 blocks

5:12 is equal to 5 blocks

if you divide them, the result is:

8/5 which is the same as 1 3/5

because 5 is contained 1 time in 8 and the rest is 3

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3 years ago
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