Finite Geometric Series
Read this topicExplanations 8
- Geometric sequences are sequences of numbers that have a common ratio between consecutive terms. Geometric series refers to the sum of the terms of a geometric sequence. Let's r…
By Cindy Zhang, Bill Zhang, Jacob Zhang, Maria Monks, Expii Team, Alex Federspiel, Joshua Siktar
- Let's suppose we want to find the sum S=1+2+4+⋯+210S = 1+2+4+\cdots+2^{10}S=1+2+4+⋯+210 We could just add everything up, but that would take too long! What might you do instead?…
By Ray Li, Moor Xu, Victor Wang
- A geometric series is a sum of numbers that follow a pattern. That pattern is that consecutive terms differ only by some common factor, denoted rrr. For instance, consider this …
By Joshua Siktar
- A geometric sequence is a recursively defined sequence of numbers where every term in the sequence (except the first) is found by multiplying the previous term by some constant …
By Rajiv Movva, Moor Xu, Anusha Rahman
- Decimal Expansion of 1/89 Warning! Expanding 1/89 is long and painful! The answer is 0.01123595505617977528089887640449438202247191‾0.\overline{011235955056179775280898876404494…
By Tommy San Miguel, Po-Shen Loh, Alex Federspiel, Laurence Putterman
- (Video) Geometric Series by GVSUmath In this video by GVSUmath, the concept of Geometric series is explained.
By Stefan Cuevas, Alex Federspiel
- সসীম গুণোত্তর ধারা হলো এমন একটি ধারা যেখানে কোন পদের সাথে তার পরবর্তী পদের অনুপাত সর্বদা সমান। যেমনঃ 5+25+125+625+…+5n5+25+125+625+ \ldots+5^n5+25+125+625+…+5n যেখানে প্রথম পদ 5…
By Thamim Zahin · বাংলা
- Finite Geometric Series As we learned earlier, a series is the sum of all the terms in a sequence. Geometric sequences are commonly expressed as recursive sequences. Each new te…
By Anusha Rahman
Problems 8
- Find the value of 2+32+54+98+1716+3332−62 + \frac32 + \frac54 + \frac98 + \frac{17}{16} + \frac{33}{32} - 62+23+45+89+1617+3233−6.
- Let an=(−2)na_n = (-2)^nan=(−2)n for all n≥0n \ge 0n≥0. Find the value of rrr which satisfies ∑n=18an=∑n=14rn2\sum_{n=1}^8 a_n = \sum_{n=1}^4 \frac{r^n}{2}n=1∑8an=n=1∑42rn
- Let nnn be a positive integer. Then it turns out 12+cosx+cos2x+⋯+cosnx=csin((2n+1)x/2)sin(x/2)\frac{1}{2} + \cos x + \cos 2x + \cdots + \cos nx = c\frac{\sin ((2n+1)x/2)}{\…
- Let x1,x2,…,x10x_1,x_2,\dots,x_{10}x1,x2,…,x10 be 101010 numbers. Suppose that xi+2xi+1=1x_i + 2 x_{i + 1} = 1xi+2xi+1=1 for each iii from 111 through 999. What is the valu…
- What is the value of the sum ∑z1∣1−z∣2,\sum_z \frac{1}{{\left|1 - z\right|}^2} ,z∑∣1−z∣21, where zzz ranges over all 7 solutions (real and nonreal) of the equation z7=−1z^7 = …
- The small town of Halloweenville was founded with a population of 100010001000 people. Assume every resident is about 000 years old at this time. Each resident lives for about 3…
- Suppose that your chance of being cast for a certain role is proportional to your skill level. If you are 111 of 100100100 people auditioning, and everyone is equal in skill lev…
- What is the value of ∑n=010an\sum\limits_{n=0}^{10} a_nn=0∑10an?