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Category > Information Systems Posted 28 Apr 2017 My Price 3.00

Number Theory

Number Theory The ancient Greeks were very interested in number patterns. Triangular numbers are numbers that can be represented by a triangular array of dots, with n dots on each side. The first three triangular numbers are 1, 3, and 6.

 

a. Find the next five triangular numbers.

b. Write a general formula for the nth term of this sequence.

c. Prove that the sum of first n triangular numbers can be found using the formula

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Alpha Geek
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Status NEW Posted 28 Apr 2017 10:04 AM My Price 3.00

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file 1493374410-2073277_1_636288874228444518_Triangular-numbers.docx preview (111 words )
N----------- va-----------lue----------- Tr-----------ian-----------gul-----------ar -----------num-----------ber----------- Fo-----------rmu-----------la ----------- 1 -----------1 =-----------1 -----------2 3----------- =1-----------+2 ----------- 3 -----------6 =-----------1+2-----------+3 ----------- 4 -----------10 -----------=1+-----------2+3-----------+4 ----------- 5 -----------15 -----------=1+-----------2+3-----------+4+-----------5 -----------6 2-----------1 =-----------1+2-----------+3+-----------4+5-----------+6 ----------- 7 -----------28 -----------=1+-----------2+3-----------+4+-----------5+6-----------+7 ----------- 8 -----------36 -----------=1+-----------2+3-----------+4+-----------5+6-----------+7+-----------8 -----------9 4-----------5 =-----------1+2-----------+3+-----------4+5-----------+6+-----------7+8-----------+9 ----------- (a-----------) -----------The----------- si-----------tua-----------tio-----------n h-----------as -----------bee-----------n e-----------xpl-----------ain-----------ed -----------in -----------the----------- di-----------agr-----------am -----------abo-----------ve.----------- W-----------e c-----------an -----------see----------- an----------- em-----------erg-----------ing----------- pa-----------tte-----------rn.----------- T-----------he -----------nth----------- tr-----------ian-----------gul-----------ar -----------num-----------ber----------- is----------- th-----------e s-----------um -----------of -----------all----------- th-----------e v-----------alu-----------es -----------of -----------n f-----------rom----------- 1 -----------to -----------n. ----------- Th-----------e f-----------irs-----------t t-----------hre-----------e t-----------ria-----------ngu-----------lar----------- nu-----------mbe-----------rs -----------are----------- 1,-----------3,6-----------. -----------The----------- ne-----------xt -----------fiv-----------e t-----------ria-----------ngu-----------lar----------- nu-----------mbe-----------rs
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