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Question

The value of i1+3+5+....+(2n+1) is _______.

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Solution

Consider the value i1+3+5+7...........(2n+1)

Let, x= 1+3+5+7......(2n+1),then i1+3+5+7...........(2n+1)=ix

…….(1)

This is A.P. series which have first term is a=1, common difference is (d)=2 and number of term is N=2n+1

Now sum of A.P. is, sn=n2[2a+(n1)d]

Thus ,

x =2n+12[2(2n+1)+(2n)2]

=2n+12[(2n+1)+(2n)]

=2n+12[(4n+1)]

x =(2n+1)(4n+1)2

Put the value of x in equation 1st

Hence,i1+3+5+7...........(2n+1)=i(2n+1)(4n+1)2


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