Find the sum of the first six terms of the geometric series 12+36+108... Find the sum of the first 10 terms of the geometric series 2+6+18+54+162+... Find the sum of the first n terms of the geometric sequence with the given values below. Simplify your answer. \f...
To find the sum of the series 3+7+14+24+37+… up to n terms, we can follow these steps: Step 1: Identify the nth termLet's denote the nth term of the series as Tn. The given series is:- T1=3- T2=7- T3=14- T4=24- T5=37 Step 2: Find the differences between consecutive...
41: Find the nth term and the sum of n term of the series 2+12+36+80+150+252+... View Solution Find the sum of the following arithmetic progressions:x−yx+y,3x−2yx+y,5x−3yx+y,.tonterms (ii)−26,−24,−22,to 36 terms. View Solution...
Find the sum of the first 100 terms for the sequence sigma_{n = 1}^{infinity} 2 / n^2 + 4n + 3 and then find the sum s. Find the sum of the first 200 terms of the arithmetic sequence 12, 9, 6, . Find the sum of ...
Infinite series: Here we just have to put the values of n and place the differences side by side and sum them all to infinity and eventually except 3 all the terms will get cancelled and the last terms of the infinite series can be ignored as they tend to zero and...
The mixed terms take proper account of the mutual influence of the two magnetic impurities (we thus ignore the self-interaction terms, which are irrelevant in the present context). In summary, we consider ΔEkσ(mixed)=J2Ω2V22mℏ2∑q(q≠k)ei(k-q)·R+e-i(k-q)·Rk2-q2〈σ∣S1...
Let a,n be positive integers, let H be a finite abelian p-group, and let G=Capn⊕H. Suppose that D(Cpn⊕H)≤2pn−1. If p>2r(H) thenη(G)=2D(G)−apn=apn+2D(H)−2 provided that H satisfies one of the following conditions: (1) D(H)≤2exp(H). (2) ⌈(k+...
The first purpose of this paper is to refine the error termsK_r(x), L_r(x)andU_r(x)from the above formulas. Therefore, let\sigma _{u} = \mathrm{id}_{u}*\mathbf{1}be the generalized divisor function for any real numberuand letm\ge 1be an integer. Then for any large positiv...
2. Which of the following shows the alternating series,$3 – \dfrac{3}{4} + \dfrac{1}{3} – \dfrac{3}{16} + …$, in terms of the summation notation in which we begin with $n = 1$? $\sum_{n=1}^{\infty} (-1)^{n}\dfrac{3}{n}$ $\sum_{n=1}^{\infty} (-1)^...
Infinite Geometric Series Sum: Sum of an infinite geometric series with {eq}a{/eq} as initial term and {eq}r{/eq} as common ratio is given by, {eq}\displaystyle \sum_{n=0}^{\infty} ar^n = \frac{a}{1-r}\text{ where }|r|<1{/eq} We can write the gi...