2 +n 10 2n 3 (-1)" 75. an n(-1)" 76. а, — 2 + п 78. а, — п3 — Зп + 3 77. an= 3 -2ne " od babnod Le) bas 79. Find the limit of the sequence 2, V2/2, V2/2/2 80. A sequence {an} is given by a1 = /2, an+ 1 = V2 + an. (a) By induction or otherwise, show that {a,} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim, an exists. (b) Find lim,n->* an . 81. Show that the sequence defined by boe i 1 = 3- an+1 a11 аn is increasing and an < 3 for all n. Deduce that {ant is conver- gent and find its limit. 82. Show that the sequence defined by 1 a1 2 an+1 3 an satisfies 0< an 2 and is decreasing. Deduce that the sequence is convergent and find its limit. l

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.