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  • Find the sum of the series 1+3+5+.........+99.

Find the sum of the series 1+3+5+.........+99.

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We note that the sum of the series is an arithmetic series with first term a=1, common difference d=2 and last term l=99.
Let there be n terms in the given series,then using
l=a+(n-1)d,we get
99=l+(n-1) imes2Rightarrow 98=2(n-1)
Rightarrow n-1=48Rightarrow n=50

herefore Sum of the series=fracn2(a+l)=frac502(1+99)

Rightarrow 25 imes100=2500

Posted by

Deependra Verma

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