Use the summation formulas to rewrite the expression withous summatiom notation. ∑i=1n4i+5n2 Use the result to find the sums for n=10, 100.

∑i=1ni=n(n+1)2 ∑i=1nk=n.k, where k=constant for n=10 ∑i=1104i+5(10)2=1100[4∑i=110i+∑i=1105] =1100[]410(10+1)2+10×5]=2.7 for n=100 ∑i=11004i+5(100)2=1(100)2[4⋅∑i=1100i+∑{i=1}1005] =1(100)2[4100(100+1)2+(5×100)] =2.07

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Calculus and Analysis
Calculus 2
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Answered question

2021-11-15

Use the summation formulas to rewrite the expression withous summatiom notation.

\sum_{i = 1}^{n} \frac{4 i + 5}{n^{2}}

Use the result to find the sums for n=10, 100.

Answer & Explanation

Mollicchiuk

Beginner2021-11-16Added 13 answers

\sum_{i = 1}^{n} i = \frac{n (n + 1)}{2}

\sum_{i = 1}^{n} k = n . k

, where k=constant
for

n = 10

\sum_{i = 1}^{10} \frac{4 i + 5}{{(10)}^{2}} = \frac{1}{100} [4 \sum_{i = 1}^{10} i + \sum_{i = 1}^{10} 5]

= \frac{1}{100} [] 4 \frac{10 (10 + 1)}{2} + 10 \times 5] = 2.7

for n=100

\sum_{i = 1}^{100} \frac{4 i + 5}{{(100)}^{2}} = \frac{1}{{(100)}^{2}} [4 \cdot \sum_{i = 1}^{100} i + \sum {i = 1}^{100} 5]

= \frac{1}{{(100)}^{2}} [4 \frac{100 (100 + 1)}{2} + (5 \times 100)]

= 2.07

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