SOLUTION: Find the sum. 1 + 4 + 16 + · ·

SOLUTION: Find the sum. 1 + 4 + 16 + · · · + 65,536

Question 1158775: Find the sum.
1 + 4 + 16 + · · · + 65,536

Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.

Use the formula for the sum of a geometric progression.

If , , , . . . , is the geometric progression with the first term " a ", the common ratio " r ", and the number of terms " n "

then the sum of its first n terms is

       = = .

Or, which is the same

       = .

In your case, a = 1, r = 4, n - 1 = = 8 (the number of the terms); n = 9.

Substitute this data into the formula and calculate.

------------------

On geometric progressions, see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

RELATED QUESTIONS
Find the general rule of the following sequence.show your solution... (answered by ikleyn)

The sum 1 - 2 + 3 - 4 + ... + 65 - 66 + 67... (answered by mananth)

find the sum of the geometric series 1 + (1/2) + (1/4) + (1/8) + (1/16) +... (answered by stanbon)

Write the series in expanded form and find the sum. 5 ∑(4j-16) j=1 A.... (answered by Edwin McCravy)

Write the expression below in expanded form and then find the sum: 3 Σ (4^k-1) (answered by Alan3354)

Find the sum of the first 8 terms in the geometric series 1-4+16-64+... (answered by richwmiller)

Find the sum of the first n terms of the following series 1-4+9-16+---- (answered by solver91311)

Find the partial sum Sn of the geometric sequence that... (answered by stanbon)

1+2+4+8+16+32+...+65,536 Find the sum of each sequence of numbers.... (answered by KMST)