Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 58

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If $x, y, z$ and $w$ are non-zero real numbers and $x^{2} + 5 y^{2} + 5 z^{2} + 4 w^{2} - 4 x y - 4 y z - 4 z w = 0$ , then $x, y, z, w$ are in

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Important Questions on Sequences and Series

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 59

\sum_{n = 0}^{\infty} \frac{(\ln x)^{n}}{n!}

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 60

The sum of

\sum_{n = 2}^{\infty} {}^{n}C_{2} \cdot \frac{3^{n - 2}}{n!}

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 61

\frac{2}{1!} + \frac{2 + 4}{2!} + \frac{2 + 4 + 6}{3!} + \frac{2 + 4 + 6 + 8}{4!} + \dots \dots . to \infty

equals

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 62

\frac{\frac{1}{2!} + \frac{1}{4!} + \frac{1}{6!} + \dots}{\frac{1}{1!} + \frac{1}{3!} + \frac{1}{5!} + \dots} =

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 63

The sum of the series

(\frac{a - b}{a}) + \frac{1}{2} {(\frac{a - b}{a})}^{2} + \frac{1}{3} {(\frac{a - b}{a})}^{3} + \dots \dots \infty

will be

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 64

\sum_{n = 0}^{\infty} \frac{n^{2} + n + 1}{(n + 1)!}

is equal to -

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 65

If

x = \frac{1}{1.2} + \frac{1}{3.4} + \frac{1}{5.6} \dots \dots \infty

, and

y = 1 - \frac{1}{2.3} - \frac{1}{4.5} - \frac{1}{6.7} \dots \dots \infty

, then

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Gamma Question Bank for Engineering Mathematics>Chapter 4 - Sequences and Series>Assignment>Q 66

If

x^{2} y = 2 x - y

and

| x | < 1

, then

\frac{(y + \frac{y^{3}}{3} + \frac{y^{5}}{5} + \dots \infty)}{(x + \frac{x^{3}}{3} + \frac{x^{5}}{5} + \dots \dots \infty)} =