Assignment 2

Problems

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1. Calculate:

\[ S = 1 + 4 + 7 + 11 +... + 100 \]

sum(seq(1 , 100, 3))

## [1] 1717

2. Calculate:

\[ S = 1^{2020} + 2^{2020} + 3^{2020} +...+2020^{2020} \]

sum((c(1:2020)^2020))

## [1] Inf

3. Calculate:

\[ S = \frac{1}{1\cdot 2}+\frac{1}{2 \cdot 3}+...+\frac{1}{2020\cdot 2021} \]

x <- c(1:2020)
y <- c(2:2021)
sum(1/(x*y))

## [1] 0.9995052

4. Calculate:

\[ S = \frac{1}{1\cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+...+\frac{1}{2020\cdot 2021 \cdot 2022} \]

z <- c(3:2022)
sum(1/(x*y*z))

## Warning in x * y * z: NAs produced by integer overflow

## [1] NA

5. Calculate:

\[ S = 1^1 + 3^3 + 5^5 + 7^7 +....+2021^{2021} \]

s <- seq(1, 2021, 2)
sum(s^s)

## [1] Inf