How to use find the sum of in a sentence? Find typical usage patterns (collocations)/phrases/context for "find the sum of" and check conjugation/comparative form for "find the sum of". Mastering all the usages of "find the sum of" from sentence examples published by news publications.
Euler was the first to find the sum of this series in 1737. Bernoulli also studied the exponential series which came out of examining compound interest. In May 1690 in a paper published in Acta Eruditorum, Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation.
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To integrate a function exactly it is required to find the sum of infinite trapezoids, but numerically only the sum of only finite trapezoids can be found, and hence the approximation of the mathematical procedure. Similarly, to differentiate a function, the differential element approaches zero but numerically only a finite value of the differential element can be chosen.
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To find the sum up to any given index, consider the binary expansion of the index, and add elements which correspond to each 1 bit in the binary form. For example, say one wishes to find the sum of the first eleven values. Eleven is 10112 in binary. This contains three 1 bits, so three elements must be added: 10002, 10102, and 10112. These contain the sums of values 1–8, 9–10, and 11, respectively.
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Find the sum of these three digits, then if there is a carry-digit from the tens-column (written in superscript under the second line in the hundreds-column) then add this carry-digit as well. If the resulting sum has one digit then write it down under the second line in the hundreds- column; if it has two digits then write the last digit down under the line in the hundreds-column, and carry the first digit over to the thousands-column, writing it as a superscript to the yet-unwritten thousands-digit under the line. Between the first and second lines, the thousands-column will contain either two or three digits: the hundreds-digit of the tens-row, the tens-digit of the hundreds-row, and (possibly) the thousands-digit of the ones-row. Find the sum of these digits, then if there is a carry-digit from the hundreds- column (written in superscript under the second line in the thousands-column) then add this carry-digit as well.
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Start with the ones-column: the ones-column should contain a pair of digits: the ones-digit of the first number and, under it, the ones-digit of the second number. Find the sum of these two digits: write this sum under the line and in the ones-column. If the sum has two digits, then write down only the ones-digit of the sum. Write the "carry digit" above the top digit of the next column: in this case the next column is the tens-column, so write a 1 above the tens-digit of the first number.
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If the resulting sum has one digit then write it down under the second line in the thousands-column; if it has two digits then write the last digit down under the line in the thousands-column, and carry the first digit over to the ten-thousands-column, writing it as a superscript to the yet-unwritten ten-thousands-digit under the line. Between the first and second lines, the ten-thousands-column will contain either one or two digits: the hundreds-digit of the hundreds-column and (possibly) the thousands-digit of the tens-column. Find the sum of these digits (if the one in the tens-row is missing think of it as a 0), and if there is a carry-digit from the thousands-column (written in superscript under the second line in the ten-thousands-column) then add this carry-digit as well. If the resulting sum has one digit then write it down under the second line in the ten-thousands- column; if it has two digits then write the last digit down under the line in the ten-thousands-column, and carry the first digit over to the hundred- thousands-column, writing it as a superscript to the yet-unwritten hundred- thousands digit under the line.
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