We can start by factoring out the constant, 16:
Σ𝑟r=1
16 (5r - 1) = 16 Σ𝑟r=1 (5r - 1)
Next, we can use the formula for the sum of the first n natural numbers:
Σ𝑟r=1 r = 1 + 2 + ... + n = n(n + 1)/2
Substituting this formula into our expression, we have:
16 Σ𝑟r=1 (5r - 1) = 16 (5(1) - 1 + 5(2) - 1 + ... + 5n - 1)
= 16 [5(1 + 2 + ... + n) - n]
= 16 [5(n(n+1)/2) - n]
= 8n(5n-1)
Therefore, the expression Σ𝑟r=1 16 (5r - 1) simplifies to 8n(5n-1).
Evaluate Σ𝑟r=1
16 (5r- 1)
1 answer