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Ifa(1),a(2),a(3),"........",a(n) are in ...

If`a_(1),a_(2),a_(3),"........",a_(n)` are in AP with `a_(1)=0`, prove that `(a_(3))/(a_(2))+(a_(4))/(a_(3))+"......"+(a_(n))/(a_(n-1))-a_(2)((1)/(a_(2))+(1)/(a_(3))"+........"+(1)/(a_(n-2)))=(a_(n-1))/(a_(2))+(a_(2))/(a_(n-1))`.

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To prove the given equation, we start by analyzing the terms in the arithmetic progression (AP) and substituting the values accordingly. ### Step-by-Step Solution: 1. **Understanding the Terms in AP**: Given that \( a_1, a_2, a_3, \ldots, a_n \) are in AP with \( a_1 = 0 \), we can express the terms as: \[ a_1 = 0, \quad a_2 = d, \quad a_3 = 2d, \quad a_4 = 3d, \ldots, \quad a_n = (n-1)d ...
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ARIHANT MATHS ENGLISH-SEQUENCES AND SERIES-Exercise (Subjective Type Questions)
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  10. If three unequel numbers are in HP and their squares are in AP, show ...

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