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and =N +(2n 1) n-. 1 +3+5+ 13. The identity (1+2+3++n) n 1 = 13 +23 +33 + .+ n3, as the first century. Provide a was known as early derivation of it. 14. Prove the following formula for the sum of triangular numbers, given by the Hindu mathematician Aryabhata (circa 500): n(n +1)(n+2) t1t2 +t3 + +tn Hint: Group the terms on the left-hand side in pairs, replacing t-1 + tk by k; consider the two cases where n is odd and n is even.] 15. Archimedes (287-212 B.C.) also derived the formula 12+22+32 + n(n + 1)(2n + 1) + n2 11 for the sum of squares. Fill in any missing details in the Hu See 8-9-74ed to3714 and Sac 3.3 # CU 9/20/19 a denvahon of (1+2+3 n ++n Hw 3.2# 13 3 Pronde n .(proof of it) t (+36 इमई टाट terte sideiDt2 n 13+23 3 n 1-1-1 otos +n nn 1-1-1 + 2 2-2 l2-1+22+*inn +6 P (I2t3+ n) n(nti) :+ग (गर स) ना h(nt) (stnen tn 4 2 hCntl)(nt2) -- t+tn Prove titt+t3+ Hint: Group the terms in LHS in pairs, replacing (consider n is odd or even) K + + Suppose n is even: (tt) (t3ttu)(tstto)tttntn J !l

and =N +(2n 1) n-. 1 +3+5+ 13. The identity (1+2+3++n) n 1 = 13 +23 +33 + .+ n3, as the first century. Provide a was known as early derivation of it. 14. Prove the following formula for the sum of triangular numbers, given by the Hindu mathematician Aryabhata (circa 500): n(n +1)(n+2) t1t2 +t3 + +tn Hint: Group the terms on the left-hand side in pairs, replacing t-1 + tk by k; consider the two cases where n is odd and n is even.] 15. Archimedes (287-212 B.C.) also derived the formula 12+22+32 + n(n + 1)(2n + 1) + n2 11 for the sum of squares. Fill in any missing details in the Hu See 8-9-74ed to3714 and Sac 3.3 # CU 9/20/19 a denvahon of (1+2+3 n ++n Hw 3.2# 13 3 Pronde n .(proof of it) t (+36 इमई टाट terte sideiDt2 n 13+23 3 n 1-1-1 otos +n nn 1-1-1 + 2 2-2 l2-1+22+*inn +6 P (I2t3+ n) n(nti) :+ग (गर स) ना h(nt) (stnen tn 4 2 hCntl)(nt2) -- t+tn Prove titt+t3+ Hint: Group the terms in LHS in pairs, replacing (consider n is odd or even) K + + Suppose n is even: (tt) (t3ttu)(tstto)tttntn J !l

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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and =N +(2n 1) n-. 1 +3+5+ 13. The identity (1+2+3++n) n 1 = 13 +23 +33 + .+ n3, as the first century. Provide a was known as early derivation of it. 14. Prove the following formula for the sum of triangular numbers, given by the Hindu mathematician Aryabhata (circa 500): n(n +1)(n+2) t1t2 +t3 + +tn Hint: Group the terms on the left-hand side in pairs, replacing t-1 + tk by k; consider the two cases where n is odd and n is even.] 15. Archimedes (287-212 B.C.) also derived the formula 12+22+32 + n(n + 1)(2n + 1) + n2 11 for the sum of squares. Fill in any missing details in the
Transcribed Image Text:and =N +(2n 1) n-. 1 +3+5+ 13. The identity (1+2+3++n) n 1 = 13 +23 +33 + .+ n3, as the first century. Provide a was known as early derivation of it. 14. Prove the following formula for the sum of triangular numbers, given by the Hindu mathematician Aryabhata (circa 500): n(n +1)(n+2) t1t2 +t3 + +tn Hint: Group the terms on the left-hand side in pairs, replacing t-1 + tk by k; consider the two cases where n is odd and n is even.] 15. Archimedes (287-212 B.C.) also derived the formula 12+22+32 + n(n + 1)(2n + 1) + n2 11 for the sum of squares. Fill in any missing details in the
Hu See 8-9-74ed to3714 and Sac 3.3 # CU 9/20/19 a denvahon of (1+2+3 n ++n Hw 3.2# 13 3 Pronde n .(proof of it) t (+36 इमई टाट terte sideiDt2 n 13+23 3 n 1-1-1 otos +n nn 1-1-1 + 2 2-2 l2-1+22+*inn +6 P (I2t3+ n) n(nti) :+ग (गर स) ना h(nt) (stnen tn 4 2 hCntl)(nt2) -- t+tn Prove titt+t3+ Hint: Group the terms in LHS in pairs, replacing (consider n is odd or even) K + + Suppose n is even: (tt) (t3ttu)(tstto)tttntn J !l
Transcribed Image Text:Hu See 8-9-74ed to3714 and Sac 3.3 # CU 9/20/19 a denvahon of (1+2+3 n ++n Hw 3.2# 13 3 Pronde n .(proof of it) t (+36 इमई टाट terte sideiDt2 n 13+23 3 n 1-1-1 otos +n nn 1-1-1 + 2 2-2 l2-1+22+*inn +6 P (I2t3+ n) n(nti) :+ग (गर स) ना h(nt) (stnen tn 4 2 hCntl)(nt2) -- t+tn Prove titt+t3+ Hint: Group the terms in LHS in pairs, replacing (consider n is odd or even) K + + Suppose n is even: (tt) (t3ttu)(tstto)tttntn J !l
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