Use Mathematical Induction to Prove the Formula for Every Positive $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

question 78

Essay

Use mathematical induction to prove the formula for every positive integer n. Show all your work. $\sum _ { i = 1 } ^ { n } i ( i + 4 ) = \frac { n ( n + 1 ) ( 2 n + 13 ) } { 6 }$

---

Definitions:

Indirect Approach

A methodology used in financial reporting, specifically in the cash flow statement, where net income is adjusted for changes in balance sheet accounts to reflect the cash transactions.

Investing Activities

Financial transactions and events related to acquiring or disposing of investments, property, plant, and equipment.

Financing Activities

Transactions involving ways in which a business obtains and repays capital, including debt, equity, and dividend payments.

Indirect Method

An approach used in cash flow statement preparation, adjusting net income for non-cash transactions, deferrals, and accruals to calculate operating cash flow.