Question

va implor urgent!! dau coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

1 + 2 + 3 + ... + 99

progresie aritmetica cu 99 termeni, a1 = 1; a99 = 99; r = 1

S99 = 99(1 + 99)/2 = 4950

1,4^4950

_______________

b)

2 + 4 + 6 + .... + 100

progresie aritmetica

a1 = 2

an = 100

r = 2

an = a1 + (n - 1)r

100 = 2 + 2(n - 1) = 2 + 2n - 2

2n = 100

n = 50 (termeni in suma)

S50 = 50(2 + 100)/2 = 2550

2,5^2550

_______________

c)

1 + 3 + 5 + ... + 101

progresie aritmetica cu a1 = 1; an = 101; r = 2

101 = 1 + 2(n - 1) = 1 + 2n - 2 = 2n - 1

2n = 102

n = 51

S51 = 51(1 + 101)/2 = 2601

2,5^2601

_____________

d)

2*3*5*7 + 1000 = 210 + 1000 = 1210

1,7^1210

Answer 2

Explicație pas cu pas :

a )

$1.4 \cdot {1.4}^{2} \cdot {1.4}^{3} \cdot ... \cdot {1.4}^{99} = \\ \\ \\ {1.4}^{1 + 2 + 3 + ... + 99} = \\ \\ \\ {1.4}^{99 \cdot 100 \div 2} = \\ \\ \\ {1.4}^{99 \cdot 50} = \\ \\ \\ {1.4}^{4950}$

b )

${2.5}^{2} \cdot {2.5}^{4} \cdot {2.5}^{6} \cdot ... \cdot {2.5}^{100} = \\ \\ \\ {2.5}^{2 + 4 + 6 + ... + 100 } = \\ \\ \\ {2.5}^{2 \cdot (1 + 2 + 3 + ... + 50)} = \\ \\ \\ {2.5}^{2 \cdot (50 \cdot 51 \div 2)} = \\ \\ \\ {2.5}^{50 \cdot 51} = \\ \\ \\ {2.5}^{2550}$

c )

$2.25 \cdot {2.25}^{3} \cdot {2.25}^{5} \cdot ... \cdot {2.25}^{101} = \\ \\ \\ {2.25}^{1 + 3 + 5 + ... + 101} = \\ \\ \\ {2.25}^{(1 + 2 + 3 + ... + 102) - (2 + 4 + 6 + ... + 102)} = \\ \\ \\ {2.25}^{(102 \cdot 103 \div 2) - 2 \cdot (1 + 2 + 3 + ... + 51)} = \\ \\ \\ {2.25}^{(51 \cdot 103) - 2 \cdot (51 \cdot 52 \div 2)} = \\ \\ \\ {2.25}^{(51 \cdot 103) - (51 \cdot 52)} = \\ \\ \\ {2.25}^{51 \cdot (103 - 52)} = \\ \\ \\ {2.25}^{51 \cdot 51} = \\ \\ \\ {2.25}^{2601}$

d )

${ {( { ({(1.7}^{2}) }^{3} )}^{5}) }^{7} \cdot {1.7}^{1000} = \\ \\ \\ {1.7}^{2 \cdot 3 \cdot 5 \cdot 7} \cdot {1.7}^{1000} = \\ \\ \\ {1.7}^{210} \cdot {1.7}^{1000} = \\ \\ \\ {1.7}^{210 + 1000} = \\ \\ \\ {1.7}^{1210}$