what is series ppt

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Series ppt

The sum of an indicated number of  terms in a  sequence is called series, for example, the sum of the first seven terms of the sequence {n²} is the series

 First seven series {n²}  ppt:

1+4+9+16+25+36+49.

Above series is also name as the 7th sum of series  {n²}

  Finite series: 

If the number of term in a series is finite, then the series is called finite series,

Infinite series : 

While a series consisting of an unlimited number of terms is termed as an infinite series.

Sum of first n terms of an arithmetic series: 

For any sequence \left \{ a_{n} \right \} we have

Sum of first n terms of an arithmetic series ppt

If \left \{ a_{n} \right \} is an A. P, then \left \{ s_{n} \right \} can be written in the form

s_{n}=a_{n}+\left ( a_{1}+d \right )+\left ( a_{2}+2d \right )+...\left ( a_{n}-2d \right )+\left ( a_{n} -d\right )+a_{n}…..    A

If we write the term of the series in the reverse order,

s_{n}=a_{n}+\left ( a_{1}-d \right )+\left ( a_{2}-2d \right )+...\left ( a_{n}+2d \right )+\left ( a_{n} +d\right )+a_{n}………. B

the sum of the n term remain same, that is

By adding A+ B equation

2s_{n}= \left ( a_{1}+a_{n} \right )+\left ( a_{1}+a_{n} \right )+...+\left ( a_{1}+a_{n} \right )+\left ( a_{1}+a_{n} \right )

=\left ( a_{1}+a_{n} \right )+\left ( a_{1}+a_{n} \right )+\left ( a_{1}+a_{n} \right )....to\, \, n\, terms

= n\left ( a_{1}+a_{n} \right )

Thus, the formula of series ppt

formula of series

= \frac{n}{2}\left [ a_{1}+a_{1}+\left ( n-1 \right )d \right ]

= \frac{n}{2}\left [2 a_{1}+\left ( n-1 \right )d \right ]

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