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Question 23 and 24, Exercise 4.7
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es 2+3 \times 2^{2}+4 \times 2^{3}+\ldots $$ The numbers $1,2,3,4,\ldots$ are in A.P. with $a=1$ and $d=1$. The numbers $1, 2, 2^2, 2^3, \ldots$ are in G.P. with first t... es is: \[ 1 + 4y + 7y^2 + 10y^3 + \ldots \] The numbers \(1, 4, 7, 10, \ldots\) are in A.P. with \(a = 1\) and \(d = 3\). The numbers \(1, y, y^2, y^3, \ldots\) are in G.P. with first
Question 25 and 26, Exercise 4.7
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\frac{7}{7^2} + \frac{10}{7^3} + \ldots \] The numbers \(1, 4, 7, 10, \ldots\) are in AP with \(a = 1\) and \(d = 3\). The numbers \(1, \frac{1}{7}, \frac{1}{7^2}, \frac{1}{7^3}, \... + \frac{19}{8} + \frac{25}{16} + \ldots \] The numbers \(1, 7, 13, 19, 25, \ldots\) are in AP with \(a = 1\) and \(d = 6\). The numbers \(1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac
Question 27 and 28, Exercise 4.7
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es\frac{1}{9}+11\times\frac{1}{27}+\ldots $$ The numbers $5,7,9,11,4,\ldots$ are in A.P. with $a=5$ and $d=7-5=2$. The numbers $1, \dfrac{1}{3}, \dfrac{1}{9}, \dfrac{1}{27}, \l... 1}{25} + 4 \times \frac{1}{125} + \ldots \] The numbers \(1, 2, 3, 4, \ldots\) are in AP with \(a = 1\) and \(d = 1\). The numbers \(1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}, \l
Question 7 and 8, Exercise 4.3
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D =====Question 8===== Find the sum of the even numbers from $2$ to $100$. ** Solution. ** Sum of the even numbers from $2$ to $100$ is $$2+4+6+...+100 (50 \text{ t... ]\\ &=2550. \end{align} Hence the sum of the even numbers from $2$ to $100$ is $2550$. GOOD ====Go to
Question 9 and 10, Exercise 4.3
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n. =====Question 9===== Find the sum of the odd numbers from $1$ to $99$. ** Solution. ** ** Solution. ** Sum of the odd numbers from $1$ to $99$ is $$1+3+5+...+99 (50 \text{ ter... 8]\\ &=2500. \end{align} Hence the sum of the odd numbers from $1$ to $99$ is $2500$. GOOD =====Question
Question 29 and 30, Exercise 4.7
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+ 7 \times x^2 + 10 \times x^3 + \ldots \] The numbers \(1, 4, 7, 10, \ldots\) are in AP with \(a = 1\) and \(d = 4 - 1 = 3\). The numbers \(1, x, x^2, x^3, \ldots\) are in GP with first t