# مجموع 1 1/2 1/3 .... 1/n

## General term formula of series 1/1 + 1/2 + 1/3 ... +1/n

ویکی‌پدیا، دانشنامهٔ آزاد ویکی‌پدیا، دانشنامهٔ آزاد مجموع جملات دنباله حسابی و هندسی مجموع جملات دنباله ها مجموع جملات دنباله ي هندسي برابر است با: S n =a(1-q n /1-q) نكته اي درباره ي دنباله هاي هندسي:(حد مجموع) در يك دنباله ي هندسي نامتناهي با جمله ي اول a وقدر نسبت q كه lql 1 ، مجموع تمام جملات آن برابر است با: S ... در ریاضیات، سری نامحدود... ۱/۱۶ + ۱/۸ + ۱/۴ + ۱/۲، یک مثال ابتدایی برای سری‌های هندسی است که مطلقاً همگرا هستند. مجموع این سری به صورت زیر می‌باشد: + + + + ⋯ = ∑ = ∞ = − = S = 1/(1-(-1/2)) = 2/3. همچنین برای سری 1 – 1/3 + 1/9 – 1/27 + 1/81… مجموع برابر 3/4 خواهد بود. حالا ببینیم متلب در این زمینه چه کمکی به ما میکند : % define your first 5 n-elements n = 0 : 4 % generate your sequence s = (-1).^n ./ 2.^n % find its sum s_to_i = sum(s) برای شروع از دنباله ها شروع می کنم که به نظرم خیلی هم راحته!!:d مجموع جملات دنباله حسابی و هندسی: در کتاب ریاضی (2) با دنباله ها آشنا شدید و امسال ادامه آن فهرست سری‌های ریاضی - ویکی‌پدیا، دانشنامهٔ آزاد ... که > و

## Sum of 1 + 1/2 + 1/3 +.... + 1/n

Lets start by taking a quick glance at the recurring pattern of $1^{3} + 2^{3} + 3^{3} + ... n^{3}$: $1^3 = 1 = 1^2$ $1^3 + 2^3 = 1 + 8 = 9 = 3^2$ $1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36 = 6^2$ Do you see a p... For example : 1/2 and 2/4 are equivalent, y/(y+1) 2 and (y 2 +y)/(y+1) 3 are equivalent as well. To calculate equivalent fraction, multiply the Numerator of each fraction, by its respective Multiplier. What is the sum of 1^3+2^3+3^3…=? 1^2+2^2+3^2+....+n^2. We know that (x+1)^3-x ^3= 3x^2+3x+1. Putting x=1,2.....n, we get . 2^3-1^3=3(1)^2+3(1)+1 . 3^3-2^3=3(2)^2+3(2)+1..... (n+1)^3-n^3=3(n)^2+3(n)+1 Find the sum of the first n terms of the series 1+2(1+1/n ... 1^2+2^2+3^2+....+n^2 = n(n+1)(2n+1)/6 does anybody know ... Find the sum of the first n terms of the series #1+2(1+1/n) +3(1+1/n)^2 + 4(1+1/n)^3.....# Using the agp ( arithmerico - geometrico progression ) sum formula? Precalculus. 2 Answers Shwetank Mauria Aug 30, 2017 #S_n=n^2# Explanation: Let us find #S_m#, the ... Solve Adding, subtracting and finding the least common ... حسابان 1 - درس 1 : مجموع جملات دنباله حسابی ... 1.3 هزار بازدید 1 سال ...

## Harmonic series (mathematics)

General term formula of series 1/1 + 1/2 + 1/3 ... +1/n Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. $$\ln(n+1)\le\sum_{i=1}^n\frac1i\le\ln(n)+1$$ This is a rather tight upper limit and lower limit you can use to approximate your answer. One could also note that $$\sum_{i=1}^n\frac1i=\int_0^1\sum_{i=0}^{n-1}x^i\ dx=\int_0^1\frac{1-x^n}{1-x}\ dx$$ We also have the Euler-Maclaurin expansion: As I know the formula for adding 1,2,3…n is given by n(n+1)/2 Comparing to above formula if we want to calculate sum up to n-1 , using the above formula we get n-1(n-1+1)/2 That is n(n-1)/2 Thus the required formula is n(n-1)/2 In mathematics, the harmonic series is the divergent infinite series ∑ = ∞ = + + + + + ⋯. Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1 / 2, 1 / 3, 1 / 4, etc., of the string's fundamental wavelength.Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase ... What is formula of 1+2+3…+(n Tinh tong S = 1 + 1/2 + 1/3 + 1/4 +.......+1/n Sum of 1 + 1/2 + 1/3 +.... + 1/n Sum of 1 + 1/2 + 1/3 +… + 1/n [duplicate] Ask Question Asked 1 year, 2 months ago. Active 1 year, 2 months ago. Viewed 28k times 4. 2 $\begingroup$ This question already has answers here: Do harmonic numbers have a “closed-form” expression? (6 answers) Closed ...

## Tinh tong S = 1 + 1/2 + 1/3 + 1/4 +.......+1/n

Proof that T(n)=n(n+1)/2 Check out Max's channel: https://youtu.be/oiKlybmKTh4Check out Fouier's way, by Dr. Peyam: https://www.youtube.com/watch?v=erfJnEsr89wSum of 1/n^2,pi^2/6, black... anyone knows proof for 1^3+2^3+3^3+...+n^3=(1+2+3...+n)^2 ... For the proof, we will count the number of dots in T(n) but, instead of summing the numbers 1, 2, 3, etc up to n we will find the total using only one multiplication and one division!. To do this, we will fit two copies of a triangle of dots together, one red and an upside-down copy in green. E.g. T(4)=1+2+3+4 + = So we can construct f(n) = f(n-1) + 1/(n(n+1)). Now look at the small values of n: f(1) = 1/2, f(2) = 1/2 + 1/6 = 2/3, f(3) = 2/3 + 1/12 = 3/4, f(4) = 3/4 + 1/20 = 4/5, etc. So for the first few small values of n, we have proven by demonstration that f(n) = n / (n+1). First establish that 1+2+3+...+n = n(n+1)/2. This is easily done. When n = 1, 1 = 1(1+1)/2, so the statement holds in this case. Suppose that for some k>=1 that I know that we are (n-1) * (n times), but why the division by 2? It's only (n - 1) * n if you use a naive bubblesort. You can get a significant savings if you notice the following: After each compare-and-swap, the largest element you've encountered will be in the last spot you were at. Proof by intuition done by Leonhard Euler, sum of 1/n^2 ... 1/(1x2)+1/(2x3)+1/(3x4)...+1/(n(n+1))