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3 years ago

I need serious help with this. Someone help me please.

Mathematics

1 answer:

GalinKa [24]3 years ago

6 0

Step-by-step explanation:

the answer is

a= 2

b=3

c= 8

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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2 years ago

15.

Lady bird [3.3K]

Answer:

$59.99

Step-by-step explanation:

11% of $59.99 is $6.60. $59.99+$6.60=66.59

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3 years ago

What is 18 divided by 2/3?

pishuonlain [190]

Division is basically
x divided by y=x/y so
18 divided by 2/3= $\frac{18}{ \frac{2}{3} }$
we want the bottom number to be =1 so we multiply 2/3 by 3/2 to make it 1 (or 6/6=1), but we have to multiply the top number by 3/2 also so that we don't change the fraction and make our work useless so

$\frac{18}{ \frac{2}{3} } times \frac{ \frac{3}{2} }{ \frac{3}{2} } = \frac{ \frac{54}{2} }{ \frac{6}{6} }= \frac{27}{1}=27$

the answe ris 27

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3 years ago

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Given : circle x with radius r and circle y with radius s

tigry1 [53]

Answer:

we need to know the variables

Step-by-step explanation:

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4 years ago

I need help with this question. It is a file.

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