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Q: Find a formula for the general term an of the sequence,

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.

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Q: Find a formula for the general term an of the sequence,

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.

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Q: (a). Let a1 = a, a2 = f (

(a). Let a1 = a, a2 = f (a), a3 = f (a2) = f (f (a))), . . ., an+1 = f (an), where f is a continuous function. If lim n→∞an = L, show that f (L) = L. (b). Illustrate part (a) by taking f (x) = cos x,...

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Q: Show that the sequence defined by satisfies 0 < an < 2

Show that the sequence defined by satisfies 0 < an < 2 and is decreasing. Deduce that the sequence is convergent and find its limit.

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Q: Find a formula for the general term an of the sequence,

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues.

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Q: Find the limit of the sequence {√2, √2√

Find the limit of the sequence {√2, √2√2, √2√2√2, …}

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Q: If you deposit $100 at the end of every month into

If you deposit $100 at the end of every month into an account that pays 3% interest per year compounded monthly, the amount of interest accumulated after months is given by the sequence (a). Find th...

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Q: If $1000 is invested at 6% interest, compounded annually

If $1000 is invested at 6% interest, compounded annually, then after years the investment is worth an = 1000 (1.06)n dollars. (a). Find the first five terms of the sequence {an}. (b). Is the sequence...

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Q: Show that the series is convergent. How many terms of the

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

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Q: Use a graph of the sequence to decide whether the sequence is

Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the sequence is convergent, guess the value of the limit from the graph and then prove your guess.

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