Calculate the sum sum_n=05 n(n+1)

May 10, 2026Mathematics

ScanSolve AI Answer

May 10, 2026

Answer

Here's how to solve the summation:

Step 1: Expand the term inside the summation. The expression is $n(n+1)$ . $n(n+1) = n^2 + n$

Step 2: Calculate each term for $n$ from 0 to 5. For $n=0: 0(0+1) = 0 \times 1 = 0$ For $n=1: 1(1+1) = 1 \times 2 = 2$ For $n=2: 2(2+1) = 2 \times 3 = 6$ For $n=3: 3(3+1) = 3 \times 4 = 12$ For $n=4: 4(4+1) = 4 \times 5 = 20$ For $n=5: 5(5+1) = 5 \times 6 = 30$

Step 3: Sum all the calculated terms. $\sum_{n=0}^{5} n(n+1) = 0 + 2 + 6 + 12 + 20 + 30$ $= 70$

The sum is $\boxed{70}$ . That's 2 down. 3 left today — send the next one.

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Quick Answer

Here's how to solve the summation: Step 1: Expand the term inside the summation. The expression is n(n+1).

Asked on May 10, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 10, 2026

Here's how to solve the summation: Step 1: Expand the term inside the summation. The expression is n(n+1). n(n+1) = n^2 + n Step 2: Calculate each term for n from 0 to 5. For n=0: 0(0+1) = 0 × 1 = 0 For n=1: 1(1+1) = 1 × 2 = 2 For n=2: 2(2+1) = 2 × 3 = 6 For n=3: 3(3+1) = 3 × 4 = 12 For n=4: 4(4+1) = 4 × 5 = 20 For n=5: 5(5+1) = 5 × 6 = 30 Step 3: Sum all the calculated terms. _n=0^5 n(n+1) = 0 + 2 + 6 + 12 + 20 + 30 = 70 The sum is 70. That's 2 down. 3 left today — send the next one.

Asked on May 10, 2026Mathematics

ScanSolve AI AnswerAnswered on May 10, 2026

Here's how to solve the summation: Step 1: Expand the term inside the summation. The expression is n(n+1). n(n+1) = n^2 + n Step 2: Calculate each term for n from 0 to 5. For n=0: 0(0+1) = 0 × 1 = 0 For n=1: 1(1+1) = 1 × 2 = 2 For n=2: 2(2+1) = 2 × 3 = 6 For n=3: 3(3+1) = 3 × 4 = 12 For n=4: 4(4+1) = 4 × 5 = 20 For n=5: 5(5+1) = 5 × 6 = 30 Step 3: Sum all the calculated terms. _n=0^5 n(n+1) = 0 + 2 + 6 + 12 + 20 + 30 = 70 The sum is 70. That's 2 down. 3 left today — send the next one.