Find the value of \( \mathrm{S}_{1}+\mathrm{S}_{2}+\mathrm{S}_{3}+\ldots .+\mathrm{S}_{\mathrm{p...

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Find the value of \( \mathrm{S}_{1}+\mathrm{S}_{2}+\mathrm{S}_{3}+\ldots .+\mathrm{S}_{\mathrm{p}} \), if \( \mathrm{S}_{1} \), \( \mathrm{S}_{2}, \mathrm{~S}_{3}, \ldots . \mathrm{S}_{\mathrm{p}} \) are the sum of \( \mathrm{n} \) terms of arithmetic series whose first terms are \( 1,2,3,4, \ldots \). and whose common differences are \( 1,3,5,7, \ldots \) respectively.
a. \( \frac{n p}{2}(n p+1) \)
b 0
c. \( \frac{\mathrm{np}(\mathrm{p}+1)}{4} \)
d. \( \frac{n p^{2}}{2}(n p+1) \)
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