In an arithmetic sequence,

MATHEMATICS · Subjective · A Level · Mathematics · Sequences and series · Sequences and series

Problem

In an arithmetic sequence, u1=1.3u_1 = 1.3, u2=1.4u_2 = 1.4 and uk=31.2u_k = 31.2. (b) Find the exact value of SkS_k. Consider the terms, unu_n, of this sequence such that n≤kn \le k. Let FF be the sum of the terms for which nn is not a multiple of 3. (c) Show that F=3240F = 3240. (d) An infinite geometric series is given as S∞=a+a2+a2+…,a∈Z+.S_{\infty} = a + \frac{a}{\sqrt{2}} + \frac{a}{2} + \dots, a \in \mathbb{Z}^{+}. Find the largest value of aa such that S∞<FS_{\infty} < F.

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