To find the sum of the infinite series S=5−73+932−1133+…, we will follow these steps: Step 1: Identify the seriesThe series can be expressed as:S=5−73+932−1133+…We can see that the numerators 5,7,9,11,… form an arithmetic progression (AP) with a common difference ...
The sum Sn of the first n terms of an AP is given by:Sn=n2×(a+l)where l is the last term. Here, the last term l is T31=0. Substituting n=31, a=20, and l=0:S31=312×(20+0)=312×20=6202=310 ConclusionThe maximum sum of the series is:310...
The formula for the first n terms of an arithmetic progression isFormula (First n Numbers in an AP): Sn = n/2 [ 2a + ( n – 1 ) d ] where Sn = sum of the n termsn = total termsa = first termd = common differenceLet us consider adding the first 30 numbers in the sequence...
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Sum Formula of Geometric Series: Examples Check Your Knowledge Lesson Summary FAQs Activities What is the formula for the sum of infinite geometric series? Where a is the initial value and r is the common ratio: a * (1/(1 - r)) Note that this formula only applies if |r|<1! If...
The formula can be remembered by recalling that for even values of n, the sum can be rearranged to n/2 pairs each adding to (n+1). What is the sum of every natural number? The sum of every natural number is an infinite series which does not converge to a specific value. Adding ...
Arithmetic Progression (AP) is a sequence of numbers in order that the common difference of any two successive numbers is a constant value. Learn with arithmetic sequence formulas and solved examples.
Homework Statement Find the sum of the first n terms of the sequence U1, U2, U3... Ur Homework Equations The Attempt at a Solution $$...
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This in turn is established by using the nonlinear version of Krein-Rutman theorem. We then obtain a characterization of the saddle-point equilibrium in terms of the corresponding HJI equation. Finally, we use a controlled population system to illustrate results. 展开 ...