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erastovalidia [21]
2 years ago
11

For each of the summations given below, use the formula for the sum of the first n integers either to evaluate the sum or to exp

ress it in closed form. (a) 9 + 10 + 11 + 12 + ... + 700 (b) 9 + 10 + 11 + 12 + ... +k
Mathematics
1 answer:
yarga [219]2 years ago
5 0

The answers are

a) 245314

b) (k2 + k- 72)/2

a)

Let F(n) denotes the sum of first n natural numbers.

F(n) = (n(n+1))/2

9+10+11+12+13+----------------------+700

F(700) - F(8) = (700*701)/2 - (8*9)/2 = 490628/2 = 245314

b)

9+10+11+-------------------k

F(k) - F(8) = (k(k+1))/2 - (8*9)/2 = (k2 + k- 72)/2

Natural numbers are all positive numbers like 1, 2, 3, 4, and so on. They are the numbers you usually count and they continue till infinity.

Learn more about natural numbers here: brainly.com/question/24672369

#SPJ4

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Step-by-step explanation:

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Given:

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Proof:

Statement                             Reason

1. AD || BC                           1. Given

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3. ∠AED ≅ ∠CEB               3. Vertical Opposite Angle Theorem.

4. AE ≅ EC                        4. Given

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Qs 9)

Given:

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Proof:

Statement                             Reason

1. AB ≅ BC                        1. Given

2. ∠ABD ≅ ∠CBD            2. Given      

3. BD ≅ BD                       3. Reflexive Property

4. ΔABD ≅ ΔCBD             4. By S-A-S congruence test

5. ∠A ≅ ∠C                       5. Corresponding parts of congruent Triangles Proved.

Qs 10)

Given:

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Statement                             Reason

1. ∠MCI ≅ ∠AIC       1. Given

2. MC ≅ AI              2. Given

3. CI ≅ CI                3. Reflexive Property

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