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Sequences and seriesAlgebraCollegeabout 0:33

Evaluate the sum of 2^k from k=0 to 10: animated lesson

A narrated, step-by-step sequences and series video lesson with captions. Final answer: 2047.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$\sum_{k=0}^{10} {2}^{ k}$
2. Step by step
1. $\sum_{k=0}^{10} {2}^{ k}$
  Write the sum
2. $1 + 2 + 4 + \cdots$
  List the first terms
3. $\sum_{k=0}^{10} {2}^{ k} = 2047$
  Add all 11 terms exactly (as fractions)
3. The answer
$\text{2047}$
Σ = 2047
4. Check
- Decimal value: 2047

Transcript

The problem. Here is the problem: sum of 2 to the power k from k equals 0 to 10. Add the terms 2 ^ k for k equals 0, 1, …, 10 (11 terms).

Step by step. Write the sum. List the first terms. Add all 11 terms exactly (as fractions).

The answer. So the answer is 2047. Each term is computed exactly and added. For long arithmetic or geometric sums a closed formula gives the same result.

Check. Decimal value: 2047.

About sequences and series

Evaluate finite sums and arithmetic and geometric series.

Evaluate the sum of 2^k from k=0 to 10: Step-by-Step Lesson