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GANITASİRASANGRAHA.
difference between the first term and the common diffurence in the series). Then) the square of the sum of the series) is multiplied by the common difference. If the first term is smaller than the oommon difference, then the first of the products obtained above is) subtracted (from the second product). If, however, the first term is) greater (than the common difference), then the first product above-mentioned is) added (to the second product). (Thus) the (required) sum of the cubes is obtained.
Examples in illustration thereof. 304. What may be the sum of the oubes when the first term is 3, the common difference 2, and the number of terins 5; or, when the first term is 5, the common difference 7, and the number of terms 6?
The rule for arriving at the sum of (a number of terms in a series wherein the terms themselves are successively) the sumns of the natural numbers (from 1 up to a specified limit, these limiting numbers being the terms in the given sories in arithmetioal progression) :
305-305}. Twice the number of terms in the given series in arithmetical progression) is diminished by one and (then) multiplied by the square of the common difference. This product is divided by six and increased by half of the common difference and also by the product of the first term and the common differeuce. The sum (so obtained) is multiplied by the number of terms as diminishod by one and then increased by the product obtained by multiplying the first term as inoreased by one by the first torm itself. The quantity (80 resulting) when multiplied by half the number of terms (in the given series) gives rise to the required sum of the series wherein the terms themselves are sums (of specified series).
305-R057. Algebraically: [ {{Sm = 2%B9+ + a0 }(m– 1) +0 (4+1)]; is the
. bum of the series in arithmetical progression, wherein esob term represents the
om of a series of natural numbers up to a limiting number, whiob is itself a member in a series in arithmetioal progression.
P4, s .
