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Worked problem · Calculus II · Unit 4A

Finite Geometric Sum: Worked Example and Solution

A complete geometric-series structure example with method choice, derivation, verification, and a common wrong approach.

1 problem8 min estimated timeFoundational to intermediate progression

Problem

  1. Evaluate ∑k=053(2)k\sum_{k=0}^{5}3(2)^k.

Complete worked solutions

Every problem has a source-matched answer and independently reviewed derivation.

01

Problem 1: Evaluate ∑k=053(2)k\sum_{k=0}^{5}3(2)^k.

Answer: 189189

Why this method: Geometric-series structure matches the mathematical structure before any algebraic cleanup.

  1. There are six terms with first term 33 and ratio 22.
  2. Using S6=3(1−26)/(1−2)S_6=3(1-2^6)/(1-2) gives 189189.

What is included

See a concise answer and full derivation for evaluate sum from k equals 0 to 5 3 (2) to the power (k).

Skills assessed

  • Geometric-series structure

Prerequisites

  • sequences
  • sigma notation
Finite Geometric Sum instructional sequence
A complete geometric-series structure example with method choice, derivation, verification, and a common wrong approach. The numbered labels and written sequence preserve meaning without relying on color.
Long description

Read the diagram from top to bottom. Each numbered box names one decision or mathematical operation. Arrows show the required order; the text labels remain the complete interpretation in print, dark mode, and nonvisual reading.

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Common errors

  • Using the infinite-sum formula without checking the common-ratio condition or the starting index.

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Supporting steps